Elliptic analogue of Vershik-Kerov limit shape
Mathematical Physics
2024-03-13 v1 High Energy Physics - Theory
Combinatorics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2403.07168,
title = {Elliptic analogue of Vershik-Kerov limit shape},
author = {Andrey Grekov and Nikita Nekrasov},
journal= {arXiv preprint arXiv:2403.07168},
year = {2024}
}
Comments
19 pages, contribution to Functional Analysis volume dedicated to the 90th anniversary of Anatoly Moiseevich Vershik