Elliptic analogue of Vershik-Kerov limit shape

2024/03/11 by Andrey Grekov, Grekov, Andrey, Nikita Nekrasov +1 · 1 citation
Chemistry · Mathematics · #14H81 #60F15 #81Q60 #Chemical Thermodynamics and Molecular Structure #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2403.07168

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and uniform measure, a U(1) case of N=2* gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric ``arcsin'' law of Vershik-Kerov and Logan-Schepp.

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