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arXiv · 2609.14217

A law of large numbers for Macdonald coherent measures

Vadim Gorin
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Abstract

We resolve a conjecture on the law of large numbers for coherent measures on Young diagrams associated with Macdonald-nonnegative specializations of the algebra of symmetric functions for all $0\le q,t<1$. We prove that row and column lengths divided by the diagram size converge to the corresponding specialization parameters. The proof combines a monomial estimate for skew Macdonald polynomials with exponential tilting and binomial decompositions obtained from the branching rule for the polynomials.

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Vadim Gorin. 2026-09-13. A law of large numbers for Macdonald coherent measures. https://arxiv.org/abs/2609.14217

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