Non-intersecting paths and Hahn orthogonal polynomial ensemble

Vadim Gorin

Non-intersecting paths and Hahn orthogonal polynomial ensemble

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arxiv 0708.2349 v1 pith:335XGFUA submitted 2007-08-17 math.PR math-phmath.COmath.MP

Vadim Gorin This is my paper · ORCID

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keywords measureprocessappropriatebulkcomputecorrelationdescribesdeterminantal

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We compute the bulk limit of the correlation functions for the uniform measure on lozenge tilings of a hexagon. The limiting determinantal process is a translation invariant extension of the discrete sine process, which also describes the ergodic Gibbs measure of an appropriate slope.

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Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures
math.PR 2025-07 conditional novelty 8.0 of 10

For fixed-q q-Racah tilings of a large hexagon, the 2D Gibbs measure collapses to a random 1D barcode staircase; the paper proves exponential concentration to a deterministic waterfall profile and conjectures the limi...

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