A. Borodin, Periodic Schur process and cylindric partitions, Duke Math. J, vol.140, issue.3, pp.391-468, 2007.

A. Borodin, Schur dynamics of the Schur processes, Adv. Math, vol.228, issue.4, pp.2268-2291, 2011.

A. Borodin and P. Ferrari, Random tilings and Markov chains for interlacing particles, 2015.

A. Borodin and P. L. Ferrari, Anisotropic growth of random surfaces in 2 + 1 dimensions, Comm. Math. Phys, vol.325, issue.2, pp.603-684, 2014.

A. Borodin and L. Petrov, Nearest neighbor Markov dynamics on Macdonald processes, Adv. Math, vol.300, pp.71-155, 2016.

C. Boutillier, J. Bouttier, G. Chapuy, S. Corteel, and S. Ramassamy, Dimers on rail yard graphs, Ann. Inst. Henri Poincaré D, vol.4, issue.4, pp.479-539, 2017.
DOI : 10.4171/aihpd/46
URL : https://hal.archives-ouvertes.fr/cea-01144118

J. Bouttier, G. Chapuy, and S. Corteel, From Aztec diamonds to pyramids: steep tilings, Trans. Amer. Math. Soc, vol.369, issue.8, pp.5921-5959, 2017.
DOI : 10.1090/tran/7169
URL : https://hal.archives-ouvertes.fr/hal-01017723

K. Bringmann and T. Friedrich, Exact and efficient generation of geometric random variates and random graphs, Automata, Languages, and Programming, vol.7965, pp.267-278, 2013.
DOI : 10.1007/978-3-642-39206-1_23
URL : http://www.mpi-inf.mpg.de/~kbringma/paper/2013ICALP-1.pdf

S. Corteel, C. Savelief, and M. Vuleti´cvuleti´c, Plane overpartitions and cylindric partitions, J. Combin. Theory Ser. A, vol.118, issue.4, pp.1239-1269, 2011.
DOI : 10.1016/j.jcta.2010.12.001
URL : https://doi.org/10.1016/j.jcta.2010.12.001

S. Desreux and E. Rémila, An optimal algorithm to generate tilings, J. Discrete Algorithms, vol.4, issue.1, pp.168-180, 2006.
DOI : 10.1016/j.jda.2005.01.003
URL : https://doi.org/10.1016/j.jda.2005.01.003

N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings, I. J. Algebraic Combin, vol.1, issue.2, pp.111-132, 1992.

N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings, II. J. Algebraic Combin, vol.1, issue.3, pp.219-234, 1992.

I. M. Gessel, Counting paths in Young's lattice, J. Statist. Plann. Inference, vol.34, issue.1, pp.125-134, 1993.
DOI : 10.1016/0378-3758(93)90038-8

J. Gravner, C. A. Tracy, and H. Widom, Limit theorems for height fluctuations in a class of discrete space and time growth models, J. Statist. Phys, vol.102, issue.5-6, pp.1085-1132, 2001.

W. Jockusch, J. Propp, and P. Shor, Random domino tilings and the arctic circle theorem, 1998.

K. Johansson, The arctic circle boundary and the Airy process, Ann. Probab, vol.33, issue.1, pp.1-30, 2005.
DOI : 10.1214/009117904000000937
URL : http://doi.org/10.1214/009117904000000937

D. E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific J. Math, vol.34, pp.709-727, 1970.
DOI : 10.2140/pjm.1970.34.709
URL : http://msp.org/pjm/1970/34-3/pjm-v34-n3-p09-s.pdf

C. Krattenthaler, Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes, Adv. in Appl. Math, vol.37, issue.3, pp.404-431, 2006.
DOI : 10.1016/j.aam.2005.12.006
URL : https://doi.org/10.1016/j.aam.2005.12.006

I. G. Macdonald, Symmetric functions and Hall polynomials, 1995.

E. Nordenstam, On the shuffling algorithm for domino tilings, Electron. J. Probab, vol.15, issue.3, pp.75-95, 2010.
DOI : 10.1214/ejp.v15-730
URL : https://doi.org/10.1214/ejp.v15-730

N. O'connell, Conditioned random walks and the RSK correspondence, J. Phys. A, vol.36, issue.12, pp.3049-3066, 2003.

A. Okounkov, Infinite wedge and random partitions, Selecta Math, vol.7, issue.1, pp.57-81, 2001.
DOI : 10.1007/pl00001398
URL : http://arxiv.org/pdf/math/9907127v3.pdf

A. Okounkov and N. Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, J. Amer. Math. Soc, vol.16, issue.3, pp.581-603, 2003.

A. Okounkov and N. Reshetikhin, Random skew plane partitions and the Pearcey process, Comm. Math. Phys, vol.269, issue.3, pp.571-609, 2007.
DOI : 10.1007/s00220-006-0128-8
URL : http://arxiv.org/pdf/math/0503508

I. Pak and A. Postnikov, Oscillating tableaux, (S p × S p )-modules, and Robinson-Schensted-Knuth correspondence, Proceedings of FPSAC '96, 1996.

J. Propp and D. Wilson, Coupling from the past: a user's guide, Microsurveys in discrete probability, vol.41, pp.181-192, 1997.

D. E. Speyer, Perfect matchings and the octahedron recurrence, J. Algebraic Comb, vol.25, issue.3, pp.309-348, 2007.

R. P. Stanley, Cambridge Studies in Advanced Mathematics, vol.2, 1999.

M. Vuleti´cvuleti´c, The shifted Schur process and asymptotics of large random strict plane partitions, International Mathematics Research Notices, p.43, 2007.

B. Young, Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds, Duke Math. J, vol.152, issue.1, pp.115-153, 2010.