N. Alon and J. H. Spencer, The probabilistic method, Wiley Series in Discrete Mathematics and Optimization, 2016.

J. Bandlow, An elementary proof of the hook formula, Electron. J. Combin, vol.15, issue.1, 2008.

, Cédric Boutillier and Béatrice deTilì ere. The critical Z-invariant Ising model via dimers: the periodic case, Probab. Theory Related Fields, vol.147, pp.379-413, 2010.

P. Biane, Representations of symmetric groups and free probability, Adv. Math, vol.138, issue.1, pp.126-181, 1998.

P. Biane, Approximate factorization and concentration for characters of symmetric groups, Internat. Math. Res. Notices, issue.4, pp.179-192, 2001.

A. Bufetov and A. Knizel, Asymptotics of random domino tilings of rectangular aztec diamonds, 2017.

I. Benjamini and R. Lyons, Yuval Peres, and Oded Schramm, Ann. Probab, vol.29, issue.1, pp.1-65, 2001.

C. Boutillier, The bead model and limit behaviors of dimer models, Ann. Probab, vol.37, issue.1, pp.107-142, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00379901

R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transferimpedances, Ann. Probab, vol.21, issue.3, pp.1329-1371, 1993.
DOI : 10.1214/aop/1176989121

URL : https://doi.org/10.1214/aop/1176989121

Y. Baryshnikov and D. Romik, Enumeration formulas for Young tableaux in a diagonal strip, Israel J. Math, vol.178, pp.157-186, 2010.
DOI : 10.1007/s11856-010-0061-6

URL : http://arxiv.org/pdf/0709.0498

H. Cohn, N. Elkies, and J. Propp, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J, vol.85, issue.1, pp.117-166, 1996.

M. Ionutçiocanionutçiocan-fontanine, I. Konvalinka, and . Pak, The weighted hook length formula, J. Combin. Theory Ser. A, vol.118, issue.6, pp.1703-1717, 2011.

S. Chhita, The height fluctuations of an off-critical dimer model on the square grid, J. Stat. Phys, vol.148, issue.1, pp.67-88, 2012.

H. Cohn, R. Kenyon, and J. Propp, A variational principle for domino tilings, J. Amer. Math. Soc, vol.14, issue.2, pp.297-346, 2001.

H. Cohn, M. Larsen, and J. Propp, The shape of a typical boxed plane partition, New York J. Math, vol.4, pp.137-165, 1998.

D. Cimasoni and N. Reshetikhin, Dimers on surface graphs and spin structures. I, Comm. Math. Phys, vol.275, issue.1, pp.187-208, 2007.

J. Dubédat and R. Gheissari, Asymptotics of height change on toroidal Temperleyan dimer models, J. Stat. Phys, vol.159, issue.1, pp.75-100, 2015.

E. Duse and A. Metcalfe, Asymptotic geometry of discrete interlaced patterns: Part I, Internat. J. Math, vol.26, issue.11, p.66, 2015.

N. D. Elkies, On the sums ? k=?? (4k + 1) ?n, Amer. Math. Monthly, vol.110, issue.7, pp.561-573, 2003.

R. Forman, Determinants of Laplacians on graphs, Topology, vol.32, issue.1, pp.35-46, 1993.

R. H. Fowler and . Rushbrooke, An attempt to extend the statistical theory of perfect solutions, Transactions of the Faraday Society, vol.33, pp.1272-1294, 1937.

J. S. Frame, G. De-b.-robinson, and R. M. Thrall, The hook graphs of the symmetric groups, Canadian J. Math, vol.6, pp.316-324, 1954.

A. Galluccio and M. Loebl, On the theory of Pfaffian orientations. I. Perfect matchings and permanents, Electron. J. Combin, vol.6, 1999.

C. Greene, A. Nijenhuis, and H. S. Wilf, A probabilistic proof of a formula for the number of Young tableaux of a given shape, Adv. in Math, vol.31, issue.1, pp.104-109, 1979.

O. Häggström, Random-cluster measures and uniform spanning trees, Stochastic Process. Appl, vol.59, issue.2, pp.267-275, 1995.

V. Ivanov and G. Olshanski, Kerov's central limit theorem for the Plancherel measure on Young diagrams, Symmetric functions 2001: surveys of developments and perspectives, vol.74, pp.93-151, 2002.

V. Ivanov and G. Olshanski, Kerov's central limit theorem for the Plancherel measure on Young diagrams, Symmetric functions 2001: surveys of developments and perspectives, vol.74, pp.93-151, 2002.

P. W. Kasteleyn, The statistics of dimers on a lattice : I. the number of dimer arrangements on a quadratic lattice, Physica, vol.27, pp.1209-1225, 1961.

P. W. Kasteleyn, Dimer statistics and phase transitions, J. Mathematical Phys, vol.4, pp.287-293, 1963.

P. W. Kasteleyn, Graph theory and crystal physics, Graph Theory and Theoretical Physics, pp.43-110, 1967.

R. Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré Probab. Statist, vol.33, issue.5, pp.591-618, 1997.

R. Kenyon, Lectures on dimers, 2009.

R. Kenyon, Spanning forests and the vector bundle Laplacian, Ann. Probab, vol.39, issue.5, pp.1983-2017, 2011.

R. Kenyon and A. Okounkov, Planar dimers and harnack curves, Duke Math. J, vol.131, issue.3, pp.499-524, 2006.

R. Kenyon and A. Okounkov, Limit shapes and the complex burgers equation, Acta mathematica, vol.199, issue.2, pp.263-302, 2007.

R. Kenyon, A. Okounkov, and S. Sheffield, Dimers and amoebae, Ann. of Math, vol.163, issue.2, pp.1019-1056, 2006.

R. W. Kenyon, J. G. Propp, and D. B. Wilson, Trees and matchings. Electron, J. Combin, vol.7, issue.1, p.25, 2000.

C. Krattenthaler, Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted, Electron. J. Combin, vol.2, 1995.

T. Kazami and K. Uchiyama, Random walks on periodic graphs, Trans. Amer. Math. Soc, vol.360, issue.11, pp.6065-6087, 2008.

R. Lyons, Y. Peres, and O. Schramm, Markov chain intersections and the loop-erased walk, Ann. Inst. H. Poincaré Probab. Statist, vol.39, issue.5, pp.779-791, 2003.

B. F. Logan and L. A. Shepp, A variational problem for random Young tableaux, Advances in Math, vol.26, issue.2, pp.206-222, 1977.

D. Maclagan, Introduction to tropical algebraic geometry, Tropical geometry and integrable systems, vol.580, pp.1-19, 2012.

A. H. Morales, I. Pak, and G. Panova, Hook Formulas for Skew Shapes I. q-analogues and bijections, 2016.

A. H. Morales, I. Pak, and G. Panova, Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications, SIAM J. Discrete Math, vol.31, issue.3, pp.1953-1989, 2017.

H. Naru, Shubert calculus and hook formula. Talk slides at 73rd

. Sem and . Lothar, Combin, Strobl, 2014.

J. Novelli, I. Pak, and A. V. Stoyanovskii, A direct bijective proof of the hook-length formula, Discrete Math. Theor. Comput. Sci, vol.1, issue.1, pp.53-67, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00955690

I. Pak, Hook length formula and geometric combinatorics, Sém. Lothar. Combin, vol.46, p.2, 2001.

R. Pemantle, Choosing a spanning tree for the integer lattice uniformly, Ann. Probab, vol.19, issue.4, pp.1559-1574, 1991.

L. Petrov, Asymptotics of random lozenge tilings via GelfandTsetlin schemes, vol.160, pp.429-487, 2014.

L. Petrov, Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field, Ann. Probab, vol.43, issue.1, pp.1-43, 2015.

B. Pittel and D. Romik, Limit shapes for random square Young tableaux, Adv. in Appl. Math, vol.38, issue.2, pp.164-209, 2007.

J. B. Remmel, Bijective proofs of formulae for the number of standard Young tableaux. Linear and Multilinear Algebra, vol.11, pp.45-100, 1982.

G. De-b.-robinson, On the Representations of the Symmetric Group, Amer. J. Math, vol.60, issue.3, pp.745-760, 1938.

D. Romik, Arctic circles, domino tilings and square Young tableaux, Ann. Probab, vol.40, issue.2, pp.611-647, 2012.

. Walter-rudin, Real and complex analysis, 1987.

P. Piotr´sniady, Gaussian fluctuations of characters of symmetric groups and of Young diagrams, vol.136, pp.263-297, 2006.

B. E. Sagan, Representations, combinatorial algorithms, and symmetric functions, Graduate Texts in Mathematics, vol.203, 2001.

C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math, vol.13, pp.179-191, 1961.

S. Sheffield, , 2003.

R. Speicher, Free probability theory and random matrices, Asymptotic combinatorics with applications to mathematical physics, vol.1815, pp.53-73, 2001.

. Combinatorics, , pp.202-204, 1974.

G. Tesler, Matchings in graphs on non-orientable surfaces, J. Combin. Theory Ser. B, vol.78, issue.2, pp.198-231, 2000.

H. N. Temperley and M. E. Fisher, Dimer problem in statistical mechanics-an exact result, Philos. Mag, vol.6, issue.8, pp.1061-1063, 1961.

A. M. Vershik, The hook formula and related identities, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), vol.172, pp.3-20, 1989.

A. M. Vershik and S. V. Kerov, Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Dokl. Akad. Nauk SSSR, vol.233, issue.6, pp.1024-1027, 1977.

W. David-bruce, Generating random spanning trees more quickly than the cover time, pp.296-303, 1996.

A. Young, On Quantitative Substitutional Analysis, Proc. London Math. Soc, vol.28, issue.2, pp.255-292, 1928.

A. Young and . Corrigenda, On Quantitative Substitutional Analysis, Proc. London Math. Soc, vol.31, issue.2, p.556, 1930.