A. Aggarwal, L. J. Guibas, J. Saxe, and P. W. Shor, A linear-time algorithm for computing the voronoi diagram of a convex polygon, Discrete & Computational Geometry, vol.9, issue.6, pp.591-604, 1989.
DOI : 10.1007/BF02187749

F. Aurenhammer and O. Schwarzkopf, A SIMPLE ON-LINE RANDOMIZED INCREMENTAL ALGORITHM FOR COMPUTING HIGHER ORDER VORONOI DIAGRAMS, International Journal of Computational Geometry & Applications, vol.02, issue.04, pp.363-381, 1992.
DOI : 10.1142/S0218195992000214

A. Baddeley, Spatial point processes and their applications, Stochastic Geometry, pp.1-75, 2007.

M. Beermann, C. Redenbach, and C. Thäle, Asymptotic shape of small cells, Mathematische Nachrichten, vol.3, issue.7, pp.737-747, 2014.
DOI : 10.1002/mana.201200328

M. B. Chen, S. J. Gortler, C. Gotsman, and C. Wormser, Distributed computation of virtual coordinates for greedy routing in sensor networks, Discrete Applied Mathematics, vol.159, issue.7, pp.544-560, 2011.
DOI : 10.1016/j.dam.2010.10.016

M. Bern, D. Eppstein, and F. Yao, THE EXPECTED EXTREMES IN A DELAUNAY TRIANGULATION, International Journal of Computational Geometry & Applications, vol.01, issue.01, pp.79-91, 1991.
DOI : 10.1142/S0218195991000074

M. Bogdanov, O. Devillers, and M. Teillaud, Hyperbolic delaunay complexes and voronoi diagrams made practical, Proceedings of the 29th annual symposium on Symposuim on computational geometry, SoCG '13, pp.67-76, 2013.
DOI : 10.1145/2462356.2462365
URL : https://hal.archives-ouvertes.fr/hal-00961390

J. Boissonnat and M. Teillaud, The hierarchical representation of objects: the Delaunay tree, Proceedings of the second annual symposium on Computational geometry , SCG '86, pp.260-268, 1986.
DOI : 10.1145/10515.10543

J. Boissonnat and M. Teillaud, On the randomized construction of the Delaunay tree, Theoretical Computer Science, vol.112, issue.2, pp.339-354, 1993.
DOI : 10.1016/0304-3975(93)90024-N
URL : https://hal.archives-ouvertes.fr/inria-00075419

J. Boissonnat, O. Devillers, and S. Hornus, Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension, Proceedings of the 25th annual symposium on Computational geometry, SCG '09, pp.208-216, 2009.
DOI : 10.1145/1542362.1542403

N. Bonichon and J. Marckert, Asymptotics of geometrical navigation on a random set of points in the plane, Advances in Applied Probability, vol.43, issue.4, pp.899-942, 2011.
DOI : 10.1239/aap/1324045692

N. Bonichon, C. Gavoille, N. Hanusse, and D. Ilcinkas, Connections between thetagraphs , Delaunay triangulations, and orthogonal surfaces, Graph Theoretic Concepts in Computer Science, pp.266-278, 2010.
DOI : 10.1007/978-3-642-16926-7_25
URL : https://hal.archives-ouvertes.fr/hal-00536710

C. Bordenave, Navigation on a Poisson point process. The Annals of Applied Probability, pp.708-746, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00070231

P. Bose and L. Devroye, Intersections with random geometric objects, Computational Geometry, vol.10, issue.3, pp.139-154, 1998.
DOI : 10.1016/S0925-7721(98)00004-2
URL : http://doi.org/10.1016/s0925-7721(98)00004-2

P. Bose and L. Devroye, On the stabbing number of a random Delaunay triangulation, Computational Geometry, vol.36, issue.2, pp.89-105, 2006.
DOI : 10.1016/j.comgeo.2006.05.005

P. Bose and P. Morin, Online Routing in Triangulations, SIAM Journal on Computing, vol.33, issue.4, pp.937-951, 2004.
DOI : 10.1137/S0097539700369387

P. Bose and P. Morin, Competitive online routing in geometric graphs, Theoretical Computer Science, vol.324, issue.2-3, pp.273-288, 2004.
DOI : 10.1016/j.tcs.2004.05.019

P. Bose, P. Morin, I. Stojmenovi?, and J. Urrutia, wireless networks, Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications , DIALM '99, pp.609-616, 2001.
DOI : 10.1145/313239.313282

P. Bose, A. Brodnik, S. Carlsson, E. Demaine, R. Fleischer et al., ONLINE ROUTING IN CONVEX SUBDIVISIONS, International Journal of Computational Geometry & Applications, vol.12, issue.04, pp.283-295, 2002.
DOI : 10.1142/S021819590200089X

P. Bose, R. Fagerberg, A. Van-renssen, and S. Verdonschot, Optimal local routing on Delaunay triangulations deened by empty equilateral triangles. arXiv preprint arXiv:1409, 2014.

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities -A nonasymptotic theory of independence
URL : https://hal.archives-ouvertes.fr/hal-00794821

A. Bowyer, Computing Dirichlet tessellations, The Computer Journal, vol.24, issue.2, pp.162-166, 1981.
DOI : 10.1093/comjnl/24.2.162
URL : http://comjnl.oxfordjournals.org/cgi/content/short/24/2/162

N. Broutin, O. Devillers, and R. Hemsley, EEciently navigating a random Delaunay triangulation Analysis of Algorithms, 2014.

N. Broutin, O. Devillers, and R. Hemsley, EEciently navigating a random Delaunay triangulation. arXiv preprint arXiv:1402, p.6148, 2014.

P. Calka, Tessellations In New perspectives in stochastic geometry, 2010.

P. Calka and N. Chenavier, Extreme values for characteristic radii of a Poisson-Voronoi Tessellation, Extremes, vol.43, issue.1, pp.1-27
DOI : 10.1007/s10687-014-0184-y
URL : https://hal.archives-ouvertes.fr/hal-00805976

M. Caroli and M. Teillaud, Computing 3D Periodic Triangulations, Algorithms-ESA 2009, pp.59-70, 2009.
DOI : 10.1007/978-3-642-04128-0_6
URL : https://hal.archives-ouvertes.fr/inria-00356871

D. Chen, L. Devroye, V. Dujmovi?, and P. Morin, Memoryless routing in convex subdivisions: Random walks are optimal, Computational Geometry, vol.45, issue.4, pp.178-185, 2012.
DOI : 10.1016/j.comgeo.2011.12.005

N. Chenavier, Valeurs etrêmes de mosaïques aléatoires, 2013.

N. Chenavier, A general study of extremes of stationary tessellations with examples, Stochastic Processes and their Applications, pp.2917-2953, 2014.
DOI : 10.1016/j.spa.2014.04.009

S. Cheng, A crash course on the Lebesgue integral and measure theory, 2008.

K. L. Clarkson and P. W. Shor, Applications of random sampling in computational geometry, II, Discrete & Computational Geometry, vol.1, issue.5, pp.387-421, 1989.
DOI : 10.1007/BF02187740

K. L. Clarkson, K. Mehlhorn, and R. Seidel, Four results on randomized incremental constructions, Computational Geometry, vol.3, issue.4, pp.185-212, 1993.
DOI : 10.1016/0925-7721(93)90009-U

T. H. Cormen and C. E. Leiserson, Introduction to Algorithms, 2001.

J. T. Cox, A. Gandoll, P. S. Griin, and H. Kesten, Greedy lattice animals i: Upper bounds. The Annals of Applied Probability, pp.1151-1169, 1993.

M. De-berg, M. Van-kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 1997.

J. Carufel, C. Dillabaugh, and A. Maheshwari, Point location in well-shaped meshes using jump-and-walk, Canadian Conference on Computational Geometry, 2011.

P. M. De-castro and O. Devillers, Walking Faster in a Triangulation
URL : https://hal.archives-ouvertes.fr/inria-00493046

P. M. De-castro and O. Devillers, Practical distribution-sensitive point location in triangulations, Computer Aided Geometric Design, vol.30, issue.5, pp.431-450, 2013.
DOI : 10.1016/j.cagd.2013.02.004
URL : https://hal.archives-ouvertes.fr/hal-00803093

L. De-floriani, B. Falcidieno, G. Nagy, and C. Pienovi, On sorting triangles in a delaunay tessellation, Algorithmica, vol.6, issue.1-6, pp.522-532, 1991.
DOI : 10.1007/BF01759057

L. De-haan and A. Ferreira, Extreme value theory. An introduction. Springer Series in Operations Research and Financial Engineering, 2006.

J. Dean and L. A. Barroso, The tail at scale, Communications of the ACM, vol.56, issue.2, pp.74-80, 2013.
DOI : 10.1145/2408776.2408794

B. Delaunay, Sur la sphere vide, Bulletin of Academy of Sciences of the USSR, vol.7, pp.793-8001, 1934.

E. D. Demaine, J. S. Mitchell, and J. O-'rourke, The open problems project: Problem 13

O. Devillers, THE DELAUNAY HIERARCHY, International Journal of Foundations of Computer Science, vol.13, issue.02, pp.163-180, 2002.
DOI : 10.1142/S0129054102001035
URL : https://hal.archives-ouvertes.fr/inria-00166711

O. Devillers and S. Pion, EEcient exact geometric predicates for Delaunay triangulations, Proceedings of the 5th Workshop on Algorithm Engineering & Experiments, pp.37-44, 2003.

O. Devillers, S. Meiser, and M. Teillaud, Fully dynamic delaunay triangulation in logarithmic expected time per operation, Computational Geometry, vol.2, issue.2, pp.55-80, 1992.
DOI : 10.1016/0925-7721(92)90025-N
URL : https://hal.archives-ouvertes.fr/hal-01180164

O. Devillers, S. Pion, and M. Teillaud, WALKING IN A TRIANGULATION, International Journal of Foundations of Computer Science, vol.13, issue.02, pp.181-199, 2002.
DOI : 10.1142/S0129054102001047
URL : https://hal.archives-ouvertes.fr/inria-00344519

L. Devroye, E. Mücke, and B. Zhu, A Note on Point Location in Delaunay Triangulations of Random Points, Algorithmica, vol.22, issue.4, pp.477-482, 1998.
DOI : 10.1007/PL00009234

L. Devroye, C. Lemaire, and J. Moreau, Expected time analysis for Delaunay point location, Computational Geometry, vol.29, issue.2, pp.61-89, 2004.
DOI : 10.1016/j.comgeo.2004.02.002

D. Dubhashi and A. Panconesi, Concentration of Measure for the Analysis of Randomized Algorithms, 2009.
DOI : 10.1017/CBO9780511581274

R. A. Dwyer, Higher-dimensional voronoi diagrams in linear expected time, Discrete & Computational Geometry, vol.43, issue.3, pp.343-367, 1991.
DOI : 10.1007/BF02574694

H. Edelsbrunner, dimensions, Proceedings of the fifth annual symposium on Computational geometry , SCG '89, pp.251-260, 1990.
DOI : 10.1145/73833.73850

C. A. Ferro and J. Segers, Inference for clusters of extreme values, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.56, issue.2, pp.545-556, 2003.
DOI : 10.1016/S0378-3758(97)00095-5

M. Franceschetti and R. Meester, Navigation in small-world networks: A scale-free continuum model, Journal of Applied Probability, pp.1173-1180, 2006.

J. Gao, L. J. Guibas, J. Hershberger, L. Zhang, and A. Zhu, Geometric spanner for routing in mobile networks, Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing , MobiHoc '01, pp.174-185, 2005.
DOI : 10.1145/501416.501424

K. Georgoulas and Y. Kotidis, Random hyperplane projection using derived dimensions, Proceedings of the Ninth ACM International Workshop on Data Engineering for Wireless and Mobile Access, MobiDE '10, pp.25-32, 2010.
DOI : 10.1145/1850822.1850827

S. Giordano and I. Stojmenovic, Position Based Routing Algorithms for Ad Hoc Networks: A Taxonomy, Ad hoc wireless networking, pp.103-136, 2004.
DOI : 10.1007/978-1-4613-0223-0_4

B. Gnedenko, Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire, The Annals of Mathematics, vol.44, issue.3, pp.423-453, 1943.
DOI : 10.2307/1968974

S. Goudsmit, Random Distribution of Lines in a Plane, Reviews of Modern Physics, vol.17, issue.2-3, pp.321-322, 1945.
DOI : 10.1103/RevModPhys.17.321

P. J. Green and R. Sibson, Computing Dirichlet Tessellations in the Plane, The Computer Journal, vol.21, issue.2, pp.168-173, 1978.
DOI : 10.1093/comjnl/21.2.168

L. Guibas and J. Stoll, Primitives for the manipulation of general subdivisions and the computation of Voronoi, ACM Transactions on Graphics, vol.4, issue.2, pp.74-123, 1985.
DOI : 10.1145/282918.282923

L. J. Guibas, D. E. Knuth, and M. Sharir, Randomized incremental construction of Delaunay and Voronoi diagrams, Algorithmica, vol.134, issue.1-6, pp.381-413, 1992.
DOI : 10.1007/BF01758770

M. Haenggi, Stochastic geometry for wireless networks, 2012.
DOI : 10.1017/CBO9781139043816

M. Haenggi, J. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti, Stochastic geometry and random graphs for the analysis and design of wireless networks. Selected Areas in Communications, IEEE Journal on, vol.27, issue.7, pp.1029-1046, 2009.

L. Heinrich, H. Schmidt, and V. Schmidt, Limit theorems for stationary tessellations with random inner cell structures, Advances in Applied Probability, vol.3, issue.01, pp.25-47, 2005.
DOI : 10.1239/aap/1035228121

N. Henze, The limit distribution for maxima of " weighted " r th-nearest-neighbour distances, The Journal of Applied Probability, vol.19, issue.2, pp.344-354, 1982.

W. Hoeeding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1214/aoms/1177730491

D. Hug, M. Reitzner, and R. Schneider, The limit shape of the zero cell in a stationary Poisson hyperplane tessellation. The Annals of Probability, pp.1140-1167, 2004.

S. Janson, Large deviation for sums of partially dependent random variables. Random Structures and Algorithms, pp.234-248, 2004.

B. Karp and H. Kung, GPSR, Proceedings of the 6th annual international conference on Mobile computing and networking , MobiCom '00, pp.243-254, 2000.
DOI : 10.1145/345910.345953

D. Kirkpatrick, Optimal Search in Planar Subdivisions, SIAM Journal on Computing, vol.12, issue.1, pp.28-35, 1983.
DOI : 10.1137/0212002

J. Kleinberg, The small-world phenomenon, Proceedings of the thirty-second annual ACM symposium on Theory of computing , STOC '00, pp.163-170, 2000.
DOI : 10.1145/335305.335325

R. Kleinberg, Geographic Routing Using Hyperbolic Space, IEEE INFOCOM 2007, 26th IEEE International Conference on Computer Communications, pp.1902-1909, 2007.
DOI : 10.1109/INFCOM.2007.221
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.5289

Y. Ko and N. H. Vaidya, Location-aided routing (LAR) in mobile ad hoc networks, Proceedings of the 4th annual ACM/IEEE international conference on Mobile computing and networking , MobiCom '98, pp.307-321, 2000.
DOI : 10.1145/288235.288252

I. Kolingerová, A small improvement in the walking algorithm for point location in a triangulation, 22nd European workshop on computational geometry, pp.221-224, 2006.

G. Kozma, Z. Lotker, M. Sharir, and G. Stupp, Geometrically aware communication in random wireless networks, Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing , PODC '04, pp.310-319, 2004.
DOI : 10.1145/1011767.1011813

E. Kranakis, H. Singh, and J. Urrutia, Compass routing on geometric networks, Proceedings of the 11th Canadian Conference on Computational Geometry. Citeseer, 1999.

F. Kuhn, R. Wattenhofer, and A. Zollinger, Asymptotically optimal geometric mobile ad-hoc routing, Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications , DIALM '02, pp.24-33, 2002.
DOI : 10.1145/570810.570814
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.6902

F. Kuhn, R. Wattenhofer, and A. Zollinger, Worst-case optimal and average-case eecient geometric ad-hoc routing, Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing, pp.267-278, 2003.
DOI : 10.1145/778415.778447
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.9724

C. L. Lawson, Software for C 1 surface interpolation, Mathematical Software III, pp.161-194, 1977.

M. Leadbetter, On extreme values in stationary sequences, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.42, issue.4, pp.289-303, 1974.
DOI : 10.1007/BF00532947

M. Leadbetter, Extremes and local dependence in stationary sequences. Probability Theory and Related Fields, pp.291-306, 1983.

M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and related properties of random sequences and processes, 1983.
DOI : 10.1007/978-1-4612-5449-2

J. Matou?ek, Lectures on discrete geometry, 2002.
DOI : 10.1007/978-1-4613-0039-7

M. Mauve, J. Widmer, and H. Hartenstein, A survey on position-based routing in mobile ad hoc networks, IEEE Network, vol.15, issue.6, pp.30-39, 2001.
DOI : 10.1109/65.967595

C. J. Mcdiarmid, Concentration, Probabilistic Methods in Algorithmic Discrete Mathematics, pp.195-248, 1998.
DOI : 10.1007/978-3-662-12788-9_6

R. E. Miles, RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANE, Proceedings of the National Academy of Sciences, vol.52, issue.4, pp.901-907, 1964.
DOI : 10.1073/pnas.52.4.901

R. E. Miles, RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANE, II, Proceedings of the National Academy of Sciences, vol.52, issue.5, pp.1157-1160, 1964.
DOI : 10.1073/pnas.52.5.1157

P. R. Morin, Online routing in geometric graphs, 2001.

E. P. Mücke, I. Saias, and B. Zhu, Fast randomized point location without preprocessing in two-and three-dimensional Delaunay triangulations, pp.274-283, 1996.

K. Mulmuley and S. Sen, Dynamic point location in arrangements of hyperplanes, Symposium on Computational Geometry, pp.132-141, 1991.

A. Okabe, B. Boots, K. Sugihara, and S. Chiu, Spatial tessellations: Concepts and applications of Voronoi diagrams, 2000.

C. H. Papadimitriou and D. Ratajczak, On a conjecture related to geometric routing, Theoretical Computer Science, vol.344, issue.1, pp.3-14, 2005.
DOI : 10.1016/j.tcs.2005.06.022

M. Penrose, Random Geometric Graphs. Oxford scholarship online, 2003.

Y. Plan and R. Vershynin, One-Bit Compressed Sensing by Linear Programming, Communications on Pure and Applied Mathematics, vol.17, issue.8, pp.1275-1297, 2013.
DOI : 10.1002/cpa.21442
URL : http://arxiv.org/abs/1109.4299

Y. Plan and R. Vershynin, Dimension Reduction by Random Hyperplane Tessellations, Discrete & Computational Geometry, vol.200, issue.2, pp.438-461, 2014.
DOI : 10.1007/s00454-013-9561-6
URL : http://arxiv.org/abs/1111.4452

F. Preparata, PLANAR POINT LOCATION REVISITED, International Journal of Foundations of Computer Science, vol.01, issue.01, 1990.
DOI : 10.1142/S0129054190000072

A. Rao, S. Ratnasamy, C. Papadimitriou, S. Shenker, and I. Stoica, Geographic routing without location information, Proceedings of the 9th annual international conference on Mobile computing and networking , MobiCom '03, pp.96-108, 2003.
DOI : 10.1145/938985.938996
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.8405

S. I. Resnick, Extreme values, regular variation, and point processes, 1987.
DOI : 10.1007/978-0-387-75953-1

C. Y. Robert, J. Segers, and C. A. Ferro, A sliding blocks estimator for the extremal index, Electronic Journal of Statistics, vol.3, issue.0, pp.993-1020, 2009.
DOI : 10.1214/08-EJS345

R. Rossignol and L. Pimentel, Greedy polyominoes and rst-passage times on random Voronoi tilings, Electronic Journal of Probability, vol.17, issue.12, pp.1-31

R. Schneider and W. Weil, Stochastic and Integral Geometry. Probability and Its Applications, 2008.
DOI : 10.1007/978-3-540-78859-1

M. Schulte and C. Thäle, The scaling limit of Poisson-driven order statistics with applications in geometric probability, Stochastic Processes and their Applications, pp.4096-4120, 2012.
DOI : 10.1016/j.spa.2012.08.011

R. Seidel, The upper bound theorem for polytopes: an easy proof of its asymptotic version, Computational Geometry, vol.5, issue.2, pp.115-116, 1995.
DOI : 10.1016/0925-7721(95)00013-Y

D. A. Spielman and S. Teng, Smoothed analysis of algorithms, Journal of the ACM, vol.51, issue.3, pp.385-463, 2004.
DOI : 10.1145/990308.990310

W. Szpankowski, Analytic Poissonization and Depoissonization, pp.442-519, 2001.
DOI : 10.1002/9781118032770.ch10

R. Vershynin, Estimation in high dimensions: a geometric perspective. arXiv preprint, 2014.

I. Weissman and S. Y. Novak, On blocks and runs estimators of the extremal index, Journal of Statistical Planning and Inference, vol.66, issue.2, pp.281-288, 1998.
DOI : 10.1016/S0378-3758(97)00095-5

G. Xia, Improved upper bound on the stretch factor of delaunay triangulations, Proceedings of the 27th annual ACM symposium on Computational geometry, SoCG '11, pp.264-273, 2011.
DOI : 10.1145/1998196.1998235

G. Xia and L. Zhang, Toward the tight bound of the stretch factor of Delaunay triangulations, Proceedings of the Canadian Conference of Computational Geometry (CCCG), 2011.

C. Yap, Towards exact geometric computation, Computational Geometry, vol.7, issue.1-2, pp.3-23, 1997.
DOI : 10.1016/0925-7721(95)00040-2

M. Yvinec, 2D triangulations, Cgal User and Reference Manual. Cgal Editorial Board, 4.4 edition, 2014.

B. Zhu, On Lawson???s Oriented Walk in Random Delaunay Triangulations, Fundamentals of Computation Theory, pp.222-233, 2003.
DOI : 10.1007/978-3-540-45077-1_21