Elliptic analogue of Vershik-Kerov limit shape

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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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Grekov et al. (Mon,) studied this question.

synapsesocial.com/papers/68e74ba6b6db6435876c485d https://doi.org/https://doi.org/10.48550/arxiv.2403.07168

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