L. Addario-berry and N. Broutin, Total progeny in killed branching random walk. Probab. Theory Related Fields, pp.265-295, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01220798

L. Addario-berry and B. Reed, Minima in branching random walks, The Annals of Probability, vol.37, issue.3, pp.1044-1079, 2009.
DOI : 10.1214/08-AOP428

URL : https://hal.archives-ouvertes.fr/hal-00795281

E. Aïdékon, Tail asymptotics for the total progeny of the critical killed branching random walk, Electronic Communications in Probability, vol.15, issue.0, pp.522-533, 2010.
DOI : 10.1214/ECP.v15-1583

E. Aïdékon, Convergence in law of the minimum of a branching random walk, The Annals of Probability, vol.41, issue.3A, pp.1362-1426, 2013.
DOI : 10.1214/12-AOP750

E. Aïdékon, Speed of the biased random walk on a Galton-Watson tree, Probab. Theory Related Fields, 2013.

E. Aïdékon, J. Berestycki, E. Brunet, and Z. Shi, The branching Brownian motion seen from its tip. Probab. Theory Related Fields, pp.405-451, 2013.

E. Aïdékon, Y. Hu, and O. Zindy, The precise tail behavior of the total progeny of a killed branching random walk, Ann. Probab, 2013.

E. Aïdékon and B. Jaffuel, Survival of branching random walks with absorption, Stochastic Processes and their Applications, vol.121, issue.9, pp.1901-1937, 2011.
DOI : 10.1016/j.spa.2011.04.006

E. Aïdékon and Z. Shi, Weak convergence for the minimal position in a branching random walk: A simple proof, Periodica Mathematica Hungarica, vol.143, issue.17, pp.43-54, 2010.
DOI : 10.1007/s10998-010-3043-x

E. Aïdékon and Z. Shi, The Seneta???Heyde scaling for the branching random walk, The Annals of Probability, vol.42, issue.3, 2013.
DOI : 10.1214/12-AOP809

T. Aita, H. Uchiyama, T. Inaoka, M. Nakajima, T. Kokubo et al., Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: Application to prolyl endopeptidase and thermolysin, Biopolymers, vol.25, issue.1, pp.64-79, 2000.
DOI : 10.1002/(SICI)1097-0282(200007)54:1<64::AID-BIP70>3.0.CO;2-R

D. Aldous and J. Pitman, The standard additive coalescent, Ann. Probab, vol.26, issue.4, pp.1703-1726, 1998.

D. Aldous and J. Pitman, Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent. Probab. Theory Related Fields, pp.455-482, 2000.

G. Alsmeyer and M. Meiners, Fixed points of inhomogeneous smoothing transforms, Journal of Difference Equations and Applications, vol.11, issue.2, 2012.
DOI : 10.1239/aap/1275055243

G. Alsmeyer and M. Meiners, Fixed points of the smoothing transform : two-sided solutions. Probab. Theory Related Fields, pp.165-199, 2013.

P. Andreoletti and P. Debs, The Number of Generations Entirely Visited for Recurrent Random Walks in a Random Environment, Journal of Theoretical Probability, vol.53, issue.1, 2013.
DOI : 10.1007/s10959-012-0449-9

P. Andreoletti and P. Debs, Spread of visited sites of a random walk along the generations of a branching process, Electronic Journal of Probability, vol.19, issue.0, 2013.
DOI : 10.1214/EJP.v19-2790

URL : https://hal.archives-ouvertes.fr/hal-00800339

L. Arguin, A. Bovier, and N. Kistler, Genealogy of extremal particles of branching Brownian motion, Communications on Pure and Applied Mathematics, vol.3, issue.2, pp.1647-1676, 2011.
DOI : 10.1002/cpa.20387

L. Arguin, A. Bovier, and N. Kistler, Poissonian statistics in the extremal process of branching Brownian motion. The Annals of Applied Probab, pp.1693-1711, 2012.

L. Arguin, A. Bovier, and N. Kistler, The extremal process of branching Brownian motion, Probability Theory and Related Fields, vol.29, issue.1, 2013.
DOI : 10.1007/s00440-012-0464-x

K. Athreya and P. Ney, Branching processes, 1972.
DOI : 10.1007/978-3-642-65371-1

M. Bachmann, Limit theorems for the minimal position in a branching random walk with independent logconcave displacements, Advances in Applied Probability, vol.32, issue.1, pp.159-176, 2000.
DOI : 10.1239/aap/1013540028

A. Basdevant and C. Goldschmidt, Asymptotics of the Allele Frequency Spectrum Associated with the Bolthausen-Sznitman Coalescent, Electronic Journal of Probability, vol.13, issue.0, pp.486-512, 2008.
DOI : 10.1214/EJP.v13-494

URL : https://hal.archives-ouvertes.fr/hal-00156487

J. Bérard and J. Gouéré, Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line, Communications in Mathematical Physics, vol.131, issue.2, pp.323-342, 2010.
DOI : 10.1007/s00220-010-1067-y

J. Bérard and J. Gouéré, Survival Probability of the Branching Random Walk Killed Below a Linear Boundary, Electronic Journal of Probability, vol.16, issue.0, pp.396-418, 2011.
DOI : 10.1214/EJP.v16-861

J. Berestycki, N. Berestycki, and J. Schweinsberg, Survival of Near-Critical Branching Brownian Motion, Journal of Statistical Physics, vol.131, issue.1, pp.833-854, 2011.
DOI : 10.1007/s10955-011-0224-9

URL : https://hal.archives-ouvertes.fr/hal-00661135

J. Berestycki, N. Berestycki, and J. Schweinsberg, Critical branching Brownian motion with absorption: survival probability, Probability Theory and Related Fields, vol.131, issue.2, 2012.
DOI : 10.1007/s00440-013-0533-9

URL : https://hal.archives-ouvertes.fr/hal-01092743

J. Berestycki, N. Berestycki, and J. Schweinsberg, The genealogy of branching Brownian motion with absorption, The Annals of Probability, vol.41, issue.2, pp.527-618, 2013.
DOI : 10.1214/11-AOP728

URL : https://hal.archives-ouvertes.fr/hal-00447444

J. Berestycki, E. Brunet, and Z. Shi, How many evolutionary histories only increase fitness ?, 2013.

J. Bertoin, The structure of the allelic partition of the total population for Galton???Watson processes with neutral mutations, The Annals of Probability, vol.37, issue.4, pp.1502-1523, 2009.
DOI : 10.1214/08-AOP441

URL : https://hal.archives-ouvertes.fr/hal-00191132

J. Bertoin, A limit theorem for trees of alleles in branching processes with rare neutral mutations, Stochastic Processes and their Applications, vol.120, issue.5, pp.678-697, 2010.
DOI : 10.1016/j.spa.2010.01.017

URL : https://hal.archives-ouvertes.fr/hal-00373262

I. Bienaymé, De la loi de multiplication et de la durée des familles, Soc. Philomat. Paris Extraits., Ser, vol.5, pp.37-39, 1845.

J. D. Biggins, The first- and last-birth problems for a multitype age-dependent branching process, Advances in Applied Probability, vol.35, issue.03, pp.446-459, 1976.
DOI : 10.1214/aoms/1177704865

J. D. Biggins, Martingale convergence in the branching random walk, Journal of Applied Probability, vol.8, issue.01, pp.25-37, 1977.
DOI : 10.2307/3212827

J. D. Biggins, The Growth and Spread of the General Branching Random Walk, The Annals of Applied Probability, vol.5, issue.4, pp.1008-1024, 1995.
DOI : 10.1214/aoap/1177004604

J. D. Biggins, How Fast Does a General Branching Random Walk Spread?, Classical and Modern Branching Processes, pp.19-39, 1994.
DOI : 10.1007/978-1-4612-1862-3_2

J. D. Biggins and A. E. Kyprianou, Seneta-Heyde norming in the branching random walk, Ann. Probab, vol.25, issue.1, pp.337-360, 1997.

J. D. Biggins and A. E. Kyprianou, Measure change in multitype branching, Advances in Applied Probability, vol.64, issue.02, pp.544-581, 2004.
DOI : 10.1214/aop/1024404291

J. D. Biggins and A. E. Kyprianou, Fixed Points of the Smoothing Transform: the Boundary Case, Electronic Journal of Probability, vol.10, issue.0, pp.609-631, 2005.
DOI : 10.1214/EJP.v10-255

J. D. Biggins, B. Lubachevsky, A. Swartz, and A. Weiss, A Branching Random Walk with a Barrier, The Annals of Applied Probability, vol.1, issue.4, pp.573-581, 1991.
DOI : 10.1214/aoap/1177005839

P. Billingsley, Convergence of Probability Measures Wiley Series in Probability and Statistics : Probability and Statistics, 1999.

A. Bovier and L. Hartung, The extremal process of two-speed branching Brownian motion, Electronic Journal of Probability, vol.19, issue.0, 2013.
DOI : 10.1214/EJP.v19-2982

M. D. Bramson, Maximal displacement of branching brownian motion, Communications on Pure and Applied Mathematics, vol.8, issue.5, pp.531-581, 1978.
DOI : 10.1002/cpa.3160310502

M. D. Bramson, Convergence of solutions of the Kolmogorov equation to traveling waves, Mem. Amer. Math. Soc, issue.285, pp.44-190, 1983.

M. D. Bramson and O. Zeitouni, Tightness for a family of recursion equations, The Annals of Probability, vol.37, issue.2, pp.615-653, 2009.
DOI : 10.1214/08-AOP414

E. Brunet and B. Derrida, Shift in the velocity of a front due to a cutoff, Physical Review E, vol.56, issue.3, pp.2597-2604, 1997.
DOI : 10.1103/PhysRevE.56.2597

E. Brunet and B. Derrida, Microscopic models of traveling wave equations, Computer Physics Communications, vol.121, issue.122, pp.121-122376, 1999.
DOI : 10.1016/S0010-4655(99)00358-6

URL : https://hal.archives-ouvertes.fr/hal-00113730

E. Brunet and B. Derrida, A Branching Random Walk Seen from the Tip, Journal of Statistical Physics, vol.159, issue.2???6, pp.420-446, 2011.
DOI : 10.1007/s10955-011-0185-z

E. Brunet, B. Derrida, A. Mueller, and S. Munier, Noisy traveling waves: Effect of selection on genealogies, Europhysics Letters (EPL), vol.76, issue.1, pp.1-7, 2006.
DOI : 10.1209/epl/i2006-10224-4

E. Brunet, B. Derrida, A. Mueller, and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts, Physical Review E, vol.73, issue.5, p.73056126, 2006.
DOI : 10.1103/PhysRevE.73.056126

F. Caravenna, A local limit theorem for random walks conditioned to stay positive. Probab. Theory Related Fields, pp.508-530, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00014641

F. Caravenna and L. Chaumont, Invariance principles for random walks conditioned to stay positive, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.44, issue.1, pp.170-190, 2008.
DOI : 10.1214/07-AIHP119

URL : https://hal.archives-ouvertes.fr/hal-00019049

B. Chauvin and A. Rouault, KPP equation and supercritical branching Brownian motion in the subcritical speed area. application to spatial tree. Probab. Theory Related Fields, pp.299-314, 1988.

X. Chen, Convergence rate of the limit theorem of a Galton???Watson tree with neutral mutations, Statistics & Probability Letters, vol.83, issue.2, pp.588-595, 2013.
DOI : 10.1016/j.spl.2012.10.029

URL : https://hal.archives-ouvertes.fr/hal-00569369

X. Chen, Scaling limit of the path leading to the leftmost particle in a branching random walk, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00827040

X. Chen, Waiting times for particles in a branching Brownian motion to reach the rightmost position, Stochastic Processes and their Applications, vol.123, issue.8, pp.3153-3182, 2013.
DOI : 10.1016/j.spa.2013.03.007

URL : https://hal.archives-ouvertes.fr/hal-00783023

K. S. Crump and J. H. Gillespie, The dispersion of a neutral allele considered as a branching process, Journal of Applied Probability, vol.32, issue.02, pp.208-218, 1976.
DOI : 10.2307/3211879

B. Derrida and D. Simon, The survival probability of a branching random walk in presence of an absorbing wall, Europhysics Letters (EPL), vol.78, issue.6, 2007.
DOI : 10.1209/0295-5075/78/60006

R. Dong, A. Gnedin, and J. Pitman, Exchangeable partitions derived from Markovian coalescents, The Annals of Applied Probability, vol.17, issue.4, pp.1172-1201, 2007.
DOI : 10.1214/105051607000000069

R. Durrett, D. Iglehart, and D. Miller, Weak Convergence to Brownian Meander and Brownian Excursion, The Annals of Probability, vol.5, issue.1, pp.117-129, 1977.
DOI : 10.1214/aop/1176995895

R. Durrett and T. M. Liggett, Fixed points of the smoothing transformation, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.39, issue.3, pp.275-301, 1983.
DOI : 10.1007/BF00532962

W. J. Ewens, The sampling theory of selectively neutral alleles, Theoretical Population Biology, vol.3, issue.1, pp.87-112, 1972.
DOI : 10.1016/0040-5809(72)90035-4

M. Fang and O. Zeitouni, Consistent Minimal Displacement of Branching Random Walks, Electronic Communications in Probability, vol.15, issue.0, pp.106-118, 2010.
DOI : 10.1214/ECP.v15-1533

M. Fang and O. Zeitouni, Slowdown for Time Inhomogeneous Branching Brownian Motion, Journal of Statistical Physics, vol.125, issue.1, pp.1-9, 2012.
DOI : 10.1007/s10955-012-0581-z

G. Faraud, Y. Hu, and Z. Shi, Almost sure convergence for stochastically biased random walks on trees. Probab. Theory Related Fields, pp.3-4621, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00767694

W. Feller, An Introduction to Probability Theory and Its Applications, 1971.

R. A. Fisher, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x

J. Franke, A. Közer, A. J. De-visser, and J. Krug, Evolutionary Accessibility of Mutational Pathways, PLoS Computational Biology, vol.331, issue.8, p.1002134, 2011.
DOI : 10.1371/journal.pcbi.1002134.s009

F. Galton and H. W. Watson, On the probability of the extinction of famillies, Journal of the Anthropological Institute of Great Britain, vol.4, pp.138-144, 1875.

N. Gantert, Y. Hu, and Z. Shi, Asymptotics for the survival probability in a killed branching random walk, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.1, pp.111-129, 2011.
DOI : 10.1214/10-AIHP362

URL : https://hal.archives-ouvertes.fr/hal-00579979

R. C. Griffiths and A. G. Pakes, An infinite-alleles version of the simple branching process, Advances in Applied Probability, vol.34, issue.03, pp.489-524, 1988.
DOI : 10.2307/1426333

J. M. Hammersley, Postulates for Subadditive Processes, The Annals of Probability, vol.2, issue.4, pp.652-680, 1974.
DOI : 10.1214/aop/1176996611

J. W. Harris and S. C. Harris, Survival probabilities for branching Brownian motion with absorption, Electronic Communications in Probability, vol.12, issue.0, pp.81-92, 2007.
DOI : 10.1214/ECP.v12-1259

J. W. Harris, S. C. Harris, and A. E. Kyprianou, Further probabilistic analysis of the Fisher???Kolmogorov???Petrovskii???Piscounov equation: one sided travelling-waves, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.42, issue.1, pp.125-145, 2006.
DOI : 10.1016/j.anihpb.2005.02.005

S. C. Harris, Traveling waves for the FKPP equation via probabilistic arguments, 1999.

S. C. Harris, M. Hesse, and A. E. Kyprianou, Branching Brownian motion in a strip: Survival near criticality, The Annals of Probability, vol.44, issue.1, 2012.
DOI : 10.1214/14-AOP972

S. C. Harris and M. I. Roberts, The many-to-few lemma and multiple spines, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.53, issue.1, 2011.
DOI : 10.1214/15-AIHP714

T. E. Harris, The Theory of Branching Processes, Die Grundlehren der Mathematischen Wissenschaften, 1963.
DOI : 10.1007/978-3-642-51866-9

P. Hegarty and A. Martinsson, On the existence of accessible paths in various models of fitness landscapes, The Annals of Applied Probability, vol.24, issue.4, 2013.
DOI : 10.1214/13-AAP949

C. C. Heyde, Extension of a Result of Seneta for the Super-Critical Galton-Watson Process, The Annals of Mathematical Statistics, vol.41, issue.2, pp.739-742, 1970.
DOI : 10.1214/aoms/1177697127

C. C. Heyde and E. Seneta, The simple branching process, a turning point test and a fundamental inequality : A historical note on I, J. Bienaymé. Biometrika, vol.59, pp.680-683, 1972.

Y. Hu, The Almost Sure Limits of the Minimal Position and the Additive Martingale in a Branching Random Walk, Journal of Theoretical Probability, vol.143, issue.17, 2013.
DOI : 10.1007/s10959-013-0494-z

URL : https://hal.archives-ouvertes.fr/hal-00755972

Y. Hu, How big is the minimum of a branching random walk ? arXiv :1305, 2013.

Y. Hu and Z. Shi, Slow movement of random walk in random environment on a regular tree, The Annals of Probability, vol.35, issue.5, pp.1978-1997, 2007.
DOI : 10.1214/009117906000001150

URL : https://hal.archives-ouvertes.fr/hal-00088407

Y. Hu and Z. Shi, A subdiffusive behavior of recurrent random walk in random environment on a regular tree, Probab. Theory Related Fields, vol.138, pp.3-4521, 2007.

Y. Hu and Z. Shi, Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees, The Annals of Probability, vol.37, issue.2, pp.742-789, 2009.
DOI : 10.1214/08-AOP419

URL : https://hal.archives-ouvertes.fr/hal-00414685

J. Imhof, Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications, Journal of Applied Probability, vol.1, issue.03, pp.500-510, 1984.
DOI : 10.1090/S0002-9947-1977-0433606-6

B. Jaffuel, The critical barrier for the survival of branching random walk with absorption, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.48, issue.4, pp.989-1009, 2012.
DOI : 10.1214/11-AIHP453

URL : https://hal.archives-ouvertes.fr/hal-00430791

M. Ji?ina, Stochastic branching processes with continuous state space, Czechoslovak Math. J, vol.8, issue.83, pp.292-313, 1958.

J. Kahane and J. Peyrière, Sur certaines martingales de Benoit Mandelbrot, Advances in Mathematics, vol.22, issue.2, pp.131-145, 1976.
DOI : 10.1016/0001-8708(76)90151-1

D. G. Kendall, Branching Processes Since 1873, Journal of the London Mathematical Society, vol.1, issue.1, pp.385-406, 1966.
DOI : 10.1112/jlms/s1-41.1.385

H. Kesten, Branching brownian motion with absorption, Stochastic Processes and their Applications, vol.7, issue.1, pp.9-47, 1978.
DOI : 10.1016/0304-4149(78)90035-2

H. Kesten and B. P. Stigum, A Limit Theorem for Multidimensional Galton-Watson Processes, The Annals of Mathematical Statistics, vol.37, issue.5, pp.1211-1223, 1966.
DOI : 10.1214/aoms/1177699266

J. F. Kingman, The First Birth Problem for an Age-dependent Branching Process, The Annals of Probability, vol.3, issue.5, 1975.
DOI : 10.1214/aop/1176996266

J. F. Kingman, A simple model for the balance between selection and mutation, Journal of Applied Probability, vol.174, issue.01, pp.1-12, 1978.
DOI : 10.1007/BF01900526

J. F. Kingman, Mathematics of Genetic Diversity, CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.34, 1980.
DOI : 10.1137/1.9781611970357

A. N. Kolmogorov, I. Petrovskii, and N. Piskunov, étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, 1937.

M. V. Kozlov, On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment, Theory of Probability & Its Applications, vol.21, issue.4, pp.813-825, 1976.
DOI : 10.1137/1121091

A. E. Kyprianou, Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis, Annales de l?Institut Henri Poincare (B) Probability and Statistics, vol.40, issue.1, pp.53-72, 2004.
DOI : 10.1016/j.anihpb.2003.06.001

S. Lalley and T. Sellke, A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion, The Annals of Probability, vol.15, issue.3, pp.1052-1061, 1987.
DOI : 10.1214/aop/1176992080

S. Lalley and T. Sellke, Traveling Waves in Inhomogeneous Branching Brownian Motions. I, The Annals of Probability, vol.16, issue.3, pp.1051-1062, 1988.
DOI : 10.1214/aop/1176991677

S. Lalley and T. Sellke, Travelling Waves in Inhomogeneous Branching Brownian Motions. II, The Annals of Probability, vol.17, issue.1, pp.116-127, 1989.
DOI : 10.1214/aop/1176991498

T. M. Liggett, R. B. Schinazi, and J. Schweinsberg, A contact process with mutations on a tree, Stochastic Processes and their Applications, vol.118, issue.3, pp.319-332, 2008.
DOI : 10.1016/j.spa.2007.04.007

Q. Liu, Fixed points of a generalized smoothing transformation and applications to the branching random walk, Advances in Applied Probability, vol.84, issue.01, pp.85-112, 1998.
DOI : 10.1090/S0002-9947-1986-0831202-5

Q. Liu, Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks, Stochastic Processes and their Applications, vol.82, issue.1, pp.61-87, 1999.
DOI : 10.1016/S0304-4149(99)00008-3

Q. Liu, Asymptotic properties and absolute continuity of laws stable by random weighted mean, Stochastic Processes and their Applications, vol.95, issue.1, pp.83-107, 2001.
DOI : 10.1016/S0304-4149(01)00092-8

Y. Liu, Z. Wen, and J. Wu, Generalized random recursive constructions and geometric properties of random fractals, Mathematische Nachrichten, vol.267, issue.1, pp.65-76, 2004.
DOI : 10.1002/mana.200310153

R. Lyons, A Simple Path to Biggins??? Martingale Convergence for Branching Random Walk, Classical and modern branching processes, pp.217-221, 1994.
DOI : 10.1007/978-1-4612-1862-3_17

R. Lyons, R. Pemantle, and Y. Peres, Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes, The Annals of Probability, vol.23, issue.3, pp.1125-1138, 1995.
DOI : 10.1214/aop/1176988176

T. Madaule, Convergence in Law for the Branching Random Walk Seen from Its Tip, Journal of Theoretical Probability, vol.18, issue.3, 2011.
DOI : 10.1007/s10959-015-0636-6

P. Maillard, Branching Brownian motion with selection of the N rightmost particles : An approximate model, 2011.

P. Maillard, Branching Brownian motion with selection, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00741368

P. Maillard, The number of absorbed individuals in branching Brownian motion with a barrier, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.2, pp.428-455, 2013.
DOI : 10.1214/11-AIHP451

URL : https://hal.archives-ouvertes.fr/hal-00472913

P. Maillard, Speed and fluctuations of N-particle branching Brownian motion with spatial selection, Probability Theory and Related Fields, vol.20, issue.30, 2013.
DOI : 10.1007/s00440-016-0701-9

P. Maillard and O. Zeitouni, Slowdown in branching Brownian motion with inhomogeneous variance, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.52, issue.3, 2013.
DOI : 10.1214/15-AIHP675

B. Mallein, Maximal displacement of a branching random walk in timeinhomogeneous environment, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01322464

R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Transactions of the American Mathematical Society, vol.309, issue.2, pp.811-829, 1988.
DOI : 10.1090/S0002-9947-1988-0961615-4

C. Mcdiarmid, Minimal Positions in a Branching Random Walk, The Annals of Applied Probability, vol.5, issue.1, pp.128-139, 1995.
DOI : 10.1214/aoap/1177004832

H. P. Mckean, Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov, Communications on Pure and Applied Mathematics, vol.44, issue.3, pp.323-331, 1975.
DOI : 10.1002/cpa.3160280302

O. Nerman, Branching processes and neutral mutations, Proceedings of the 1st World Congress of the Bernoulli Society, pp.683-692, 1986.

J. Neveu, Multiplicative Martingales for Spatial Branching Processes, Seminar on Stochastic Processes, pp.223-242, 1987.
DOI : 10.1007/978-1-4684-0550-7_10

S. Nowak and J. Krug, Accessibility percolation on n-trees, EPL (Europhysics Letters), vol.101, issue.6, p.66004, 2013.
DOI : 10.1209/0295-5075/101/66004

J. Pitman, Combinatorial stochastic processes., volume 1875 of Lecture Notes in Mathematics, Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, 2002.

Y. Ren and T. Yang, Limit theorem fro derivative martingale at criticality w.r.t. branching Brownian motion, Statist. Probab. Lett, vol.81, issue.2, pp.195-200, 2011.

D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999.

M. I. Roberts, Fine asymptotics for the consistent maximal displacement of branching Brownian motion, Electronic Journal of Probability, vol.20, issue.0, 2012.
DOI : 10.1214/EJP.v20-2912

M. I. Roberts, A simple path to asymptotics for the frontier of a branching Brownian motion, The Annals of Probability, vol.41, issue.5, pp.3518-3541, 2013.
DOI : 10.1214/12-AOP753

M. I. Roberts and L. Z. Zhao, Increasing paths in trees, 2013.

R. B. Schinazi and J. Schweinsberg, Spatial and non-spatial stochastic models for immune response. Markov Process, pp.255-276, 2008.

E. Seneta, On Recent Theorems Concerning the Supercritical Galton-Watson Process, The Annals of Mathematical Statistics, vol.39, issue.6, 1968.
DOI : 10.1214/aoms/1177698037

Z. Taïb, Branching Processes and Neutral Evolution, Lecture Notes in Biomathematics, vol.93, 1992.
DOI : 10.1007/978-3-642-51536-1

E. C. Waymire and S. C. Williams, A general decomposition theory for random cascades, Bulletin of the American Mathematical Society, vol.31, issue.2, pp.31216-222, 1994.
DOI : 10.1090/S0273-0979-1994-00521-X