We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.
Nous montrons en utilisant des chemins qui ne s'intersectent pas qu'un pavage rhombique d'un hexagone, ou une partition planaire en boîtes, est décrit par un point processus ponctuel déterminentiel, donné par un noyau de Hahn étendu.
Keywords: Non-intersecting paths, Dysons's Brownian motion, planar partitions, random tiling, determintal process
Mot clés : chemins qui ne s'intersectent pas, mouvement brownien de Dyson, partitions planaires, pavages aléatoires, processus déterminentiels
@article{AIF_2005__55_6_2129_0, author = {Johansson, Kurt}, title = {Non-intersecting, simple, symmetric \- random walks and the extended {Hahn} kernel}, journal = {Annales de l'Institut Fourier}, pages = {2129--2145}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {6}, year = {2005}, doi = {10.5802/aif.2155}, mrnumber = {2187949}, zbl = {1083.60079}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2155/} }
TY - JOUR AU - Johansson, Kurt TI - Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel JO - Annales de l'Institut Fourier PY - 2005 SP - 2129 EP - 2145 VL - 55 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2155/ DO - 10.5802/aif.2155 LA - en ID - AIF_2005__55_6_2129_0 ER -
%0 Journal Article %A Johansson, Kurt %T Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel %J Annales de l'Institut Fourier %D 2005 %P 2129-2145 %V 55 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2155/ %R 10.5802/aif.2155 %G en %F AIF_2005__55_6_2129_0
Johansson, Kurt. Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel. Annales de l'Institut Fourier, Volume 55 (2005) no. 6, pp. 2129-2145. doi : 10.5802/aif.2155. http://archive.numdam.org/articles/10.5802/aif.2155/
[1] Special Functions, Encyclopedia of Mathematics and its applications, 71, Cambridge University Press, Cambridge, 1999 | MR | Zbl
[2] Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles (math.CA/0310278, http://arxiv.org/abs/math.CA/0310278)
[3] The shape of a typical boxed plane partition, New York J. of Math., Volume 4 (1998), pp. 137-165 | MR | Zbl
[4] A Brownian-Motion Model for the eigenvalues of a Random Matrix, J. Math. Phys., Volume 3 (1962), pp. 1191-1198 | DOI | MR | Zbl
[5] Matrices coupled in a chain I: Eigenvalue correlations, J. of Phys. A, Volume 31 (1998), pp. 4449-4456 | DOI | MR | Zbl
[6] Step fluctuations for a faceted crystal, J. Stat. Phys., Volume 113 (2003), pp. 1-46 | DOI | MR | Zbl
[7] Correlations for the orthogonal-unitary and symplectic-unitary transitions at the soft and hard edges, Nucl. Phys. B, Volume 553 (1999), pp. 601-643 | DOI | MR | Zbl
[8] On a discrete Rodrigues' formula and a second class of orthogonal Hahn polynomials (Preprint, Department of Mathematics, Chalmers University of Technology, N° 1977-12)
[9] Discrete orthogonal polynomial ensembles and the Plancherel measure, Annals of Math., Volume 153 (2001), pp. 259-296 | DOI | MR | Zbl
[10] Non-intersecting paths, random tilings and random matrices, Probab.Theory Relat. Fields, Volume 123 (2002), pp. 225-280 | DOI | MR | Zbl
[11] Discrete polynuclear growth and determinantal processes, Commun. Math. Phys., Volume 242 (2003), pp. 277-329 | MR | Zbl
[12] The Arctic circle and the Airy process (math.PR/0306216, to appear in Ann. Probab., http://arxiv.org/abs/math.PR/0306216) | MR | Zbl
[13] Scaling limit of vicious walks and two-matrix model, Phys. Rev. E (2002)
[14] Local statistics of lattice dimers, Ann. Inst. H. Poincaré, Probabilités et Statistiques, Volume 33 (1997), pp. 591-618 | DOI | Numdam | MR | Zbl
[15] Random Matrices, 2nd ed., Academic Press, San Diego, 1991 | MR | Zbl
[16] Classical Orthogonal Polynomials of a Discrete Variable, Springer Series in Computational Physics, Berlin Heidelberg, Berlin Heidelberg, 1991 | MR | Zbl
[17] Scale invariance of the PNG droplet and the Airy process, J. Stat. Phys., Volume 108 (2002), pp. 1076-1106 | MR | Zbl
[18] Enumerative Combinatorics, Cambridge University Press, Volume 2 (1999) | Zbl
[19] Nonintersecting Paths, Pfaffians, and Plane Partitions, Adv. in Math., Volume 83 (1990), pp. 96-131 | DOI | MR | Zbl
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