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arXiv · 2409.14124

Correlation Function of Self-Conjugate Partitions: $q$-Difference Equation and Quasimodularity

Zhiyong Wang·Chenglang Yang
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Abstract

In this paper, we study the uniform measure for the self-conjugate partitions. We derive the $q$-difference equation which is satisfied by the $n$-point correlation function related to the uniform measure. As applications, we give explicit formulas for the one-point and two-point functions, and study their quasimodularity. Motivated by this, we also prove the quasimodularity of the general $n$-point function using a combinatorial method. Finally, we derive the limit shape of self-conjugate partitions under the Gibbs uniform measure and compare it to the leading asymptotics of the one-point function.

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Zhiyong Wang, Chenglang Yang. 2024-09-21. Correlation Function of Self-Conjugate Partitions: $q$-Difference Equation and Quasimodularity. https://arxiv.org/abs/2409.14124

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