Lozenge tilings of a hexagon and \(q\)-Racah ensembles

Geometric probability and stochastic geometry (60D05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Cites Work

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Universality of mesoscopic fluctuations for orthogonal polynomial ensembles
The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles
Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field
\(q\)-distributions on boxed plane partitions
A periodic hexagon tiling model and non-Hermitian orthogonal polynomials
Minimizers of convex functionals arising in random surfaces
Orthogonal polynomial ensembles in probability theory
Nonintersecting paths and the Hahn orthogonal polynomial ensemble
The shape of a typical boxed plane partition
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
Asymptotics of random domino tilings of rectangular Aztec diamonds
On global fluctuations for non-colliding processes
Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions
Hodge decomposition. A method for solving boundary value problems
Multivariable \(q\)-Racah polynomials
Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices
Polynomial ensembles and recurrence coefficients
Coupling functions for domino tilings of Aztec diamonds
Limit shapes and the complex Burgers equation
The arctic circle boundary and the Airy process
Dimers and amoebae
Non-intersecting, simple, symmetric random walks and the extended Hahn kernel.
A variational principle for domino tilings
Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients
Hypergeometric Orthogonal Polynomials and Their q-Analogues
Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings