Correlation Function of Self-Conjugate Partitions: $q$-Difference Equation and Quasimodularity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913083880898560 |
|---|---|
| author | Wang, Zhiyong Yang, Chenglang |
| author_facet | Wang, Zhiyong Yang, Chenglang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Correlation Function of Self-Conjugate Partitions: $q$-Difference Equation and Quasimodularity Wang, Zhiyong Yang, Chenglang Mathematical Physics Combinatorics Probability 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. |
| title | Correlation Function of Self-Conjugate Partitions: $q$-Difference Equation and Quasimodularity |
| topic | Mathematical Physics Combinatorics Probability |
| url | https://arxiv.org/abs/2409.14124 |