M. Aizenman, R. Sims, and S. Warzel, Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Probab. Theory Related Fields, pp.363-394, 2006.

S. Akbari, E. Ghorbani, and S. Zare, Some relations between rank, chromatic number and energy of graphs, Discrete Mathematics, vol.309, issue.3, pp.601-605, 2009.
DOI : 10.1016/j.disc.2008.09.012

D. Aldous, Asymptotic Fringe Distributions for General Families of Random Trees, The Annals of Applied Probability, vol.1, issue.2, pp.228-266, 1991.
DOI : 10.1214/aoap/1177005936

D. Aldous, The ?(2) limit in the random assignment problem, Random Structures and Algorithms, vol.8, issue.4, pp.381-418, 2001.
DOI : 10.1002/rsa.1015

D. Aldous and A. Bandyopadhyay, A survey of max-type recursive distributional equations, The Annals of Applied Probability, vol.15, issue.2, pp.1047-1110, 2005.
DOI : 10.1214/105051605000000142

D. Aldous and R. Lyons, Processes on Unimodular Random Networks, Electronic Journal of Probability, vol.12, issue.0, pp.1454-1508, 2007.
DOI : 10.1214/EJP.v12-463

D. Aldous and M. Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, Probability on discrete structures, pp.1-72, 2004.
DOI : 10.1007/978-3-662-09444-0_1

O. Angel, Growth and percolation on the uniform infinite planar triangulation, Geometric and Functional Analysis, vol.13, issue.5, pp.935-974, 2003.
DOI : 10.1007/s00039-003-0436-5

O. Angel and O. Schramm, Uniform Infinite Planar Triangulations, Communications in Mathematical Physics, vol.28, issue.2-3, pp.191-213, 2003.
DOI : 10.1007/s00220-003-0932-3

URL : http://arxiv.org/abs/math/0207153

J. Aronson, A. Frieze, and B. G. , Maximum matchings in sparse random graphs: Karp-Sipser revisited. Random Structures Algorithms, pp.111-177, 1998.

K. B. Athreya and P. E. Ney, Branching processes, 2004.
DOI : 10.1007/978-3-642-65371-1

Z. Bai and J. W. Silverstein, Spectral analysis of large dimensional random matrices, 2010.
DOI : 10.1007/978-1-4419-0661-8

A. Bandyopadhyay and D. Gamarnik, Counting without sampling, Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm , SODA '06, pp.452-479, 2008.
DOI : 10.1145/1109557.1109655

M. Bauer and O. Golinelli, On the kernel of tree incidence matrices, J. Integer Seq, vol.3, issue.1, 2000.

M. Bauer and O. Golinelli, Exactly Solvable Model with Two Conductor-Insulator Transitions Driven by Impurities, Physical Review Letters, vol.86, issue.12, pp.2621-2624, 2001.
DOI : 10.1103/PhysRevLett.86.2621

URL : https://hal.archives-ouvertes.fr/hal-00021794

M. Bauer and O. Golinelli, Random incidence matrices: moments of the spectral density, Journal of Statistical Physics, vol.103, issue.1/2, pp.301-337, 2001.
DOI : 10.1023/A:1004879905284

URL : https://hal.archives-ouvertes.fr/hal-00021795

M. Bayati, D. Gamarnik, D. Katz, C. Nair, and P. Tetali, Simple deterministic approximation algorithms for counting matchings, Proceedings of the thirty-ninth annual ACM symposium on Theory of computing , STOC '07, p.127, 2007.
DOI : 10.1145/1250790.1250809

M. Bayati and C. Nair, A rigorous proof of the cavity method for counting matchings, Proc. of the 44th Annual Allerton Conference on Communication, Control and Computing, 2006.

E. A. Bender and E. R. Canfield, The asymptotic number of labeled graphs with given degree sequences, Journal of Combinatorial Theory, Series A, vol.24, issue.3, pp.296-307, 1978.
DOI : 10.1016/0097-3165(78)90059-6

I. Benjamini and O. Schramm, Recurrence of distributional limits of finite planar graphs, Electron. J. Probab, vol.6, issue.13, p.pp, 2001.

I. Benjamini, O. Schramm, and A. Shapira, Every minor-closed property of sparse graphs is testable, STOC, pp.393-402, 2008.

J. Berg, On the absence of phase transition in the monomer-dimer model, 1998.

J. Bertoin and V. Sidoravicius, The Structure of Typical Clusters in Large Sparse Random Configurations, Journal of Statistical Physics, vol.12, issue.1, pp.87-105, 2009.
DOI : 10.1007/s10955-009-9728-y

URL : https://hal.archives-ouvertes.fr/hal-00339779

S. Bhamidi, S. N. Evans, and A. Sen, Spectra of large random trees. arXiv:0903.3589v2 [math, 2009.

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

T. Bohman and A. Frieze, Karp???Sipser on Random Graphs with a Fixed Degree Sequence, Combinatorics, Probability and Computing, vol.1, issue.05, 2009.
DOI : 10.1073/pnas.0937490100

B. Bollobás, A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs, European Journal of Combinatorics, vol.1, issue.4, pp.311-316, 1980.
DOI : 10.1016/S0195-6698(80)80030-8

B. Bollobás, Random graphs, volume 73 of Cambridge Studies in Advanced Mathematics, 2001.

B. Bollobás, S. Janson, and O. Riordan, The Cut Metric, Random Graphs, and Branching Processes, Journal of Statistical Physics, vol.81, issue.2, pp.289-335, 2010.
DOI : 10.1007/s10955-010-9982-z

B. Bollobás and O. Riordan, Sparse graphs: Metrics and random models. Random Structures & Algorithms, 2010.

C. Bordenave and M. Lelarge, Resolvent of large random graphs. Random Structures Algorithms, pp.332-352, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00948945

C. Bordenave, M. Lelarge, and J. Salez, Matchings on infinite graphs, Probability Theory and Related Fields, vol.14, issue.4
DOI : 10.1007/s00440-012-0453-0

URL : https://hal.archives-ouvertes.fr/hal-00935246

C. Bordenave, M. Lelarge, and J. Salez, The rank of diluted random graphs, The Annals of Probability, vol.39, issue.3, pp.1097-1121, 2011.
DOI : 10.1214/10-AOP567

URL : https://hal.archives-ouvertes.fr/hal-00630917

C. Borgs, J. Chayes, J. Kahn, and L. Lovász, Left and right convergence of graphs with bounded degree Arxiv preprint arXiv, 2010.

B. Borovi?anin and I. Gutman, Nullity of graphs, Zb. Rad. (Beogr.), vol.13, issue.21, pp.107-122, 2009.

A. Braunstein, M. Mézard, and R. Zecchina, Survey propagation: an algorithm for satisfiability. Random Structures Algorithms, pp.201-226, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00008893

T. Britton, M. Deijfen, and A. Martin-löf, Generating Simple Random Graphs with Prescribed Degree Distribution, Journal of Statistical Physics, vol.66, issue.6, pp.1377-1397, 2006.
DOI : 10.1007/s10955-006-9168-x

P. Chassaing and B. Durhuus, Local limit of labeled trees and expected volume growth in a random quadrangulation, The Annals of Probability, vol.34, issue.3, pp.879-917, 2006.
DOI : 10.1214/009117905000000774

URL : https://hal.archives-ouvertes.fr/hal-00137910

Y. Choe, J. Oxley, A. Sokal, and D. Wagner, Homogeneous multivariate polynomials with the half-plane property, Advances in Applied Mathematics, vol.32, issue.1-2, pp.88-187, 2004.
DOI : 10.1016/S0196-8858(03)00078-2

F. R. Chung, Spectral graph theory, CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, 1997.
DOI : 10.1090/cbms/092

Y. Colin-de-verdière, Spectres de graphes, of Cours Spécialisés [Specialized Courses]. Société Mathématique de France, 1998.

K. P. Costello, T. Tao, and V. Vu, Random symmetric matrices are almost surely nonsingular, Duke Mathematical Journal, vol.135, issue.2, pp.395-413, 2006.
DOI : 10.1215/S0012-7094-06-13527-5

URL : http://arxiv.org/abs/math/0505156

K. P. Costello and V. H. Vu, The rank of random graphs. Random Structures Algorithms, pp.269-285, 2008.

D. M. Cvetkovi?, M. Doob, and H. Sachs, Spectra of graphs, Theory and applications, 1995.

G. Davidoff, P. Sarnak, and A. Valette, Elementary number theory, group theory, and Ramanujan graphs, 2003.
DOI : 10.1017/CBO9780511615825

A. Dembo and A. Montanari, Gibbs measures and phase transitions on sparse random graphs, Brazilian Journal of Probability and Statistics, vol.24, issue.2, pp.137-211, 2010.
DOI : 10.1214/09-BJPS027

A. Dembo and A. Montanari, Ising models on locally tree-like graphs, The Annals of Applied Probability, vol.20, issue.2, pp.565-592, 2010.
DOI : 10.1214/09-AAP627

URL : https://hal.archives-ouvertes.fr/hal-00290779

A. Dembo and O. Zeitouni, Large deviations techniques and applications, volume 38 of Stochastic Modelling and Applied Probability, 1998.

L. Devroye, Branching Processes and Their Applications in the Analysis of Tree Structures and Tree Algorithms, Probabilistic methods for algorithmic discrete mathematics, pp.249-314, 1998.
DOI : 10.1007/978-3-662-12788-9_7

I. Dumitriu and S. Pal, Sparse regular random graphs: spectral density and eigenvectors. arXiv:0910.5306v3 [math, 2009.
DOI : 10.1214/11-aop673

URL : http://arxiv.org/abs/0910.5306

R. Durrett, Random graph dynamics. Cambridge Series in Statistical and Probabilistic Mathematics, 2007.

G. Elek, Note on limits of finite graphs, Combinatorica, vol.15, issue.5, pp.503-507, 2007.
DOI : 10.1007/s00493-007-2214-8

P. Erd?s and A. Rényi, On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl, vol.5, pp.17-61, 1960.

D. Gamarnik, Linear phase transition in random linear constraint satisfaction problems. Probab. Theory Related Fields, pp.410-440, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01183947

D. Gamarnik, T. Nowicki, and G. Swirszcz, Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method, Random Structures and Algorithms, vol.5, issue.2, pp.76-106, 2006.
DOI : 10.1002/rsa.20072

E. N. Gilbert, Random Graphs, The Annals of Mathematical Statistics, vol.30, issue.4, pp.1141-1144, 1959.
DOI : 10.1214/aoms/1177706098

G. R. Grimmett, Random labelled trees and their branching networks, Journal of the Australian Mathematical Society, vol.15, issue.02, pp.229-23781, 1980.
DOI : 10.1007/BF01896073

T. E. Harris, The theory of branching processes. Dover Phoenix Editions Corrected reprint of the 1963 original, p.163361, 2002.

O. Heilmann and E. Lieb, Theory of monomer-dimer systems, Communications in Mathematical Physics, vol.24, issue.4, pp.190-232, 1972.
DOI : 10.1007/BF01877590

R. V. Hofstad, Random Graphs and Complex Networks, 2011.

J. Kahn and J. H. Kim, Random Matchings in Regular Graphs, COMBINATORICA, vol.18, issue.2, pp.201-226, 1998.
DOI : 10.1007/PL00009817

J. Kahn and M. Neiman, Negative correlation and log-concavity. Random Structures Algorithms, pp.367-388, 2010.
DOI : 10.1002/rsa.20292

URL : http://arxiv.org/abs/0712.3507

R. Karp and M. Sipser, Maximum matching in sparse random graphs, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981), pp.364-375, 1981.
DOI : 10.1109/SFCS.1981.21

O. Khorunzhy, M. Shcherbina, and V. Vengerovsky, Eigenvalue distribution of large weighted random graphs, Journal of Mathematical Physics, vol.45, issue.4, pp.1648-1672, 2004.
DOI : 10.1063/1.1667610

A. Klein, Extended States in the Anderson Model on the Bethe Lattice, Advances in Mathematics, vol.133, issue.1, pp.163-184, 1998.
DOI : 10.1006/aima.1997.1688

L. Lovász and M. Plummer, Matching theory, 2009.
DOI : 10.1090/chel/367

R. Lyons, Random Walks and Percolation on Trees, The Annals of Probability, vol.18, issue.3, pp.931-958, 1990.
DOI : 10.1214/aop/1176990730

R. Lyons, Asymptotic Enumeration of Spanning Trees, Combinatorics, Probability and Computing, vol.14, issue.4, pp.491-522, 2005.
DOI : 10.1017/S096354830500684X

R. Lyons and Y. Peres, Probability on Trees and Networks, 2011.
DOI : 10.1017/9781316672815

E. Maneva, E. Mossel, and M. J. Wainwright, A new look at survey propagation and its generalizations, Journal of the ACM, vol.54, issue.4, p.pp, 2007.
DOI : 10.1145/1255443.1255445

B. D. Mckay, The expected eigenvalue distribution of a large regular graph, Linear Algebra and its Applications, vol.40, pp.203-216, 1981.
DOI : 10.1016/0024-3795(81)90150-6

B. D. Mckay and N. C. Wormald, Uniform generation of random regular graphs of moderate degree, Journal of Algorithms, vol.11, issue.1, pp.52-67, 1990.
DOI : 10.1016/0196-6774(90)90029-E

M. Mézard and A. Montanari, Information, physics, and computation. Oxford Graduate Texts, 2009.

M. Mézard and G. Parisi, The Bethe lattice spin glass revisited, The European Physical Journal B, vol.20, issue.2, pp.217-233, 2001.
DOI : 10.1007/PL00011099

M. Mézard and G. Parisi, The cavity method at zero temperature, Journal of Statistical Physics, vol.111, issue.1/2, pp.1-34, 2003.
DOI : 10.1023/A:1022221005097

M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond, World Scientific Lecture Notes in Physics, vol.9, 1987.

B. Mohar, The spectrum of an infinite graph, Linear Algebra and its Applications, vol.48, pp.245-256, 1982.
DOI : 10.1016/0024-3795(82)90111-2

B. Mohar and M. Omladi?, The spectrum of infinite graphs with bounded vertex degrees, Graphs, hypergraphs and applications (Eyba, pp.122-125, 1984.

B. Mohar and W. Woess, A Survey on Spectra of infinite Graphs, Bulletin of the London Mathematical Society, vol.21, issue.3, pp.209-234, 1989.
DOI : 10.1112/blms/21.3.209

M. Molloy and B. Reed, A critical point for random graphs with a given degree sequence Random Graphs '93, Proceedings of the Sixth International Seminar on Random Graphs and Probabilistic Methods in Combinatorics and Computer Science, pp.161-179, 1993.

A. Montanari, E. Mossel, and A. Sly, The weak limit of ising models on locally tree-like graphs. Probability Theory and Related Fields, pp.1-21

V. Müller, On the spectrum of an infinite graph, Linear Algebra and its Applications, vol.93, pp.187-189, 1987.
DOI : 10.1016/S0024-3795(87)90324-7

R. Pemantle, Towards a theory of negative dependence, Probabilistic techniques in equilibrium and nonequilibrium statistical physics, pp.1371-1390, 2000.
DOI : 10.1063/1.533200

M. Reed and B. Simon, Methods of modern mathematical physics. I. Functional analysis, 1972.

M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, 1975.

T. Richardson and R. Urbanke, The capacity of low-density parity-check codes under message-passing decoding, IEEE Transactions on Information Theory, vol.47, issue.2, pp.599-618, 2001.
DOI : 10.1109/18.910577

D. Ruelle, Counting unbranched subgraphs, Journal of Algebraic Combinatorics, vol.9, issue.2, pp.157-160, 1999.
DOI : 10.1023/A:1018690328814

J. Salez, The cavity method for counting subgraphs subject to local constraints . arXiv pre-print 1103, p.3281
URL : https://hal.archives-ouvertes.fr/inria-00577234

O. Schramm, Hyperfinite Graph Limits, Electron. Res. Announc. Math. Sci, vol.15, pp.17-23, 2008.
DOI : 10.1007/978-1-4419-9675-6_19

URL : http://arxiv.org/abs/0711.3808

A. Schrijver, Combinatorial optimization, Polyhedra and efficiency. Algorithms and Combinatorics, vol.24, pp.1-38

B. Simon, The Classical Moment Problem as a Self-Adjoint Finite Difference Operator, Advances in Mathematics, vol.137, issue.1, pp.82-203, 1998.
DOI : 10.1006/aima.1998.1728

J. M. Steele, Minimal Spanning Trees for Graphs with Random Edge Lengths, Mathematics and computer science, II (Versailles Trends Math, pp.223-245, 2002.
DOI : 10.1007/978-3-0348-8211-8_14

M. Talagrand, An assignment problem at high temperature, The Annals of Probability, vol.31, issue.2, pp.818-848, 2003.
DOI : 10.1214/aop/1048516537

M. Talagrand, Spin glasses: a challenge for mathematicians Cavity and mean field models, Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics, 2003.

L. Tran, V. Vu, and K. Wang, Sparse random graphs: Eigenvalues and eigenvectors . arXiv:1011.6646v1 [math, 2010.

L. Valiant, The complexity of computing the permanent, Theoretical Computer Science, vol.8, issue.2, pp.189-201, 1979.
DOI : 10.1016/0304-3975(79)90044-6

C. Van-nuffelen, Rank, clique and chromatic number of a graph, System modeling and optimization, pp.605-611, 1981.
DOI : 10.1007/BFb0006185

D. Wagner, Negatively Correlated Random Variables and Mason???s Conjecture for Independent Sets in Matroids, Annals of Combinatorics, vol.12, issue.2, pp.211-239, 2008.
DOI : 10.1007/s00026-008-0348-z

D. Wagner, Weighted enumeration of spanning subgraphs with degree constraints, Journal of Combinatorial Theory, Series B, vol.99, issue.2, pp.347-357, 2009.
DOI : 10.1016/j.jctb.2008.07.007

E. P. Wigner, The collected works of Eugene Paul Wigner. Part A. The scientific papers Nuclear physics Annotated by Herman Feshbach, 1996.

N. C. Wormald, Models of Random Regular Graphs, Surveys in combinatorics, pp.239-298, 1999.
DOI : 10.1017/CBO9780511721335.010

L. Zdeborová and M. Mézard, The number of matchings in random graphs, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.05, p.5003, 2006.
DOI : 10.1088/1742-5468/2006/05/P05003