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A law of large numbers for Macdonald coherent measures
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≤ 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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BibTeX
@misc{gorin2026large,
title = {{A law of large numbers for Macdonald coherent measures}},
author = {Vadim Gorin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14217},
eprint = {2609.14217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14217},
}
RIS
TY - UNPB
TI - A law of large numbers for Macdonald coherent measures
AU - Vadim Gorin
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14217
UR - https://arxiv.org/abs/2609.14217
AB - 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≤ 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.
ER -