J. Baik, T. Kriecherbauer, K. D. , T. Mclaughlin, and P. D. Miller, Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results, Int. Math. Res. Not, pp.821-858, 2003.

L. Bartholdi and W. Woess, Spectral Computations on Lamplighter Groups and Diestel-Leader Graphs, Journal of Fourier Analysis and Applications, vol.11, issue.2, pp.175-202, 2005.
DOI : 10.1007/s00041-005-3079-0
URL : http://arxiv.org/abs/math/0405182

P. Billingsley, Convergence of probability measures, Probability and measure, 1968.
DOI : 10.1002/9780470316962

R. Burton and R. Pemantle, Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings Via Transfer-Impedances, The Annals of Probability, vol.21, issue.3, pp.1329-1371, 1993.
DOI : 10.1214/aop/1176989121

R. Carmona and J. Lacroix, Spectral theory of random Schrödinger operators, Probability and its Applications, 1990.

R. Cerf and R. Kenyon, The Low-Temperature Expansion of the Wulff Crystal in the 3D Ising Model, Communications in Mathematical Physics, vol.222, issue.1, pp.147-179, 2001.
DOI : 10.1007/s002200100505

H. Cohn, R. Kenyon, and J. Propp, A variational principle for domino tilings, Journal of the American Mathematical Society, vol.14, issue.02, pp.297-346, 2001.
DOI : 10.1090/S0894-0347-00-00355-6

D. J. Daley, D. Vere, and -. , An introduction to the theory of point processes, 1988.

B. Detilì-ere, Dimères sur les graphes isoradiaux & modèles d'interfaces aléatoires en dimension 2+2, 2004.

N. P. Dolbilin, Y. M. Zinov, ?. Ev, A. S. Mishchenko, M. A. Shtan et al., Homological Properties of Dimer Configurations for Lattices on Surfaces, Funktsional'nyi Analiz i ego prilozheniya, vol.30, issue.3, pp.19-33, 1996.
DOI : 10.4213/faa535

F. J. Dyson, A Brownian???Motion Model for the Eigenvalues of a Random Matrix, Journal of Mathematical Physics, vol.3, issue.6, pp.1191-1198, 1962.
DOI : 10.1063/1.1703862

P. L. Ferrari and H. Spohn, Step fluctuations for a faceted crystal, Journal of Statistical Physics, vol.113, issue.1/2, pp.1-46, 2003.
DOI : 10.1023/A:1025703819894

M. E. Fisher, On the Dimer Solution of Planar Ising Models, Journal of Mathematical Physics, vol.7, issue.10, pp.1776-1781, 1966.
DOI : 10.1063/1.1704825

R. H. Fowler and G. S. Rushbrooke, An attempt to extend the statistical theory of perfect solutions, Transactions of the Faraday Society, vol.33, pp.1272-1294, 1937.
DOI : 10.1039/tf9373301272

Y. V. Fyodorov, Introduction to the random matrix theory: Gaussian Unitary Ensemble and beyond, p.412017, 2004.
DOI : 10.1017/CBO9780511550492.003

I. Gessel and G. Viennot, Binomial determinants, paths, and hook length formulae, Advances in Mathematics, vol.58, issue.3, pp.300-321, 1985.
DOI : 10.1016/0001-8708(85)90121-5

J. Glimm and A. Jaffe, Quantum physics, 1981.
DOI : 10.1007/978-1-4684-0121-9

]. R. Grigorchuk and A. Zuk, The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geometriae Dedicata, vol.87, issue.1/3, pp.209-244, 2001.
DOI : 10.1023/A:1012061801279

I. M. Guelfand, N. Y. Vilenkin, and L. Distributions, Tome 4: Applications de l'analyse harmonique, 1967.

K. Johansson, Non-intersecting paths, random tilings and random matrices, Probab. Theory Related Fields The arctic circle boundary and the Airy process, Ann. Probab, vol.123, issue.33, pp.225-280, 2002.
DOI : 10.1007/s004400100187
URL : http://arxiv.org/abs/math/0011250

S. Karlin and J. Mcgregor, Coincidence probabilities, Pacific Journal of Mathematics, vol.9, issue.4, pp.1141-1164, 1959.
DOI : 10.2140/pjm.1959.9.1141

P. W. Kasteleyn, Dimer Statistics and Phase Transitions, Journal of Mathematical Physics, vol.4, issue.2, pp.287-293, 1963.
DOI : 10.1063/1.1703953

M. Katori, T. Nagao, and H. Tanemura, Infinite systems of non-colliding Brownian particles, in Stochastic analysis on large scale interacting systems, Adv. Stud. Pure Math. Math. Soc. Japan, vol.39, pp.283-306, 2004.

R. Kenyon, arXiv:math-ph/9910002. [29] , Dominos and the Gaussian free field The Laplacian and Dirac operators on critical planar graphs, arXiv:math.CO/0105054. [28] , Conformal invariance of domino tiling, Ann. Probab, pp.591-618, 1997.

R. Kenyon and A. Okounkov, Planar dimers and Harnack curves, Duke Mathematical Journal, vol.131, issue.3, 2003.
DOI : 10.1215/S0012-7094-06-13134-4
URL : http://arxiv.org/abs/math/0311062

R. Kenyon, J. Propp, and D. Wilson, Trees and matchings, Electron, J. Combin . Research Paper, vol.7, issue.34, 2000.

R. Kenyon, S. Sheffield, and J. Dimers, Dimers, tilings and trees, Journal of Combinatorial Theory, Series B, vol.92, issue.2, pp.295-317, 2004.
DOI : 10.1016/j.jctb.2004.07.001
URL : http://doi.org/10.1016/j.jctb.2004.07.001

A. N. Kolmogorov, Osnovnye ponyatiya teorii veroyatnostei, Izdat, Probability Theory and Mathematical Statistics Series, vol.16, 1974.

M. Mattera, Annihilating random walks and perfect matchings of planar graphs, Discrete random walks Discrete Math, pp.173-180, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01183921

B. Mccoy and F. Wu, The two-dimensional Ising model, 1973.

G. Mikhalkin, Amoebas of algebraic varieties and tropical geometry, in Different faces of geometry, Int. Math. Ser, pp.257-300, 2004.

G. Mikhalkin and H. Rullgård, Amoebas of maximal area, Internat. Math. Res. Notices, pp.441-451, 2001.

T. Nagao and P. J. Forrester, Multilevel dynamical correlation functions for Dyson's Brownian motion model of random matrices, Physics Letters A, vol.247, issue.1-2, pp.42-46, 1998.
DOI : 10.1016/S0375-9601(98)00602-1

S. Nakamura, Lifshitz Tail for Schr??dinger Operator??with Random Magnetic Field, Communications in Mathematical Physics, vol.214, issue.3, pp.565-572, 2000.
DOI : 10.1007/s002200000276

A. Okounkov and N. Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, Journal of the American Mathematical Society, vol.16, issue.03, pp.581-603, 2003.
DOI : 10.1090/S0894-0347-03-00425-9

H. Osada, Dirichlet form approach to infinite-dimensional Wiener processes with singular interactions, Communications in Mathematical Physics, vol.103, issue.Nos. 3/4, pp.117-131, 1996.
DOI : 10.1007/BF02099365

M. Passare and H. Rullgård, Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope, Duke Math, J, vol.121, pp.481-507, 2004.

L. Pastur and A. Figotin, Spectra of random and almost-periodic operators, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1992.
DOI : 10.1007/978-3-642-74346-7

M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process, in In and out of equilibrium, pp.185-204, 2000.

J. Propp, Generalized domino-shuffling, Theoretical Computer Science, vol.303, issue.2-3, pp.267-301, 2002.
DOI : 10.1016/S0304-3975(02)00815-0

D. Revelle, Heat Kernel Asymptotics on the Lamplighter Group, Electronic Communications in Probability, vol.8, issue.0, pp.142-154, 2003.
DOI : 10.1214/ECP.v8-1092

]. S. Sheffield, Gaussian Free Field for mathematicians arXiv:math.PR/0312099, Random Surfaces: Large Deviations Principles and Gradient Gibbs Measure Classifications, 2003.

A. Soshnikov, Determinantal random point fields, Uspekhi Mat, Nauk, vol.55, pp.107-160, 2000.

A. Soshnikov, Gaussian Limit for Determinantal Random Point Fields, The Annals of Probability, vol.30, issue.1, pp.171-187, 2002.
DOI : 10.1214/aop/1020107764

H. Spohn, Interacting Brownian particles: a study of Dyson's model, in Hydrodynamic behavior and interacting particle systems, Math. Appl, vol.9, pp.151-179, 1986.

H. N. Temperley, Enumeration of graphs on a large periodic lattice, Combinatorics (Proc. British Combinatorial Conf, pp.155-159, 1973.
DOI : 10.1017/CBO9780511662072.024

H. N. Temperley and M. E. Fisher, Dimer problem in statistical mechanics-an exact result, Philosophical Magazine, vol.6, issue.68, pp.1061-1063, 1961.
DOI : 10.1039/df9531500057

G. Tesler, Matchings in Graphs on Non-orientable Surfaces, Journal of Combinatorial Theory, Series B, vol.78, issue.2, pp.198-231, 2000.
DOI : 10.1006/jctb.1999.1941

W. P. Thurston, Conway's Tiling Groups, The American Mathematical Monthly, vol.97, issue.8, pp.97-757, 1990.
DOI : 10.2307/2324578

D. B. Wilson, Generating random spanning trees more quickly than the cover time, Proceedings of the twenty-eighth annual ACM symposium on Theory of computing , STOC '96, pp.296-303, 1996.
DOI : 10.1145/237814.237880