Confluent hypergeometric kernel determinant on multiple large intervals
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909736797995008 |
|---|---|
| author | Xu, Taiyang Zhang, Lun Zhao, Zhengyang |
| author_facet | Xu, Taiyang Zhang, Lun Zhao, Zhengyang |
| contents | The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig singular point for a broad class of unitary ensembles. It is the aim of this work to investigate large gap asymptotics of this process over a union of disjoint intervals $\cup_{j=0}^{n}(sa_j,sb_j)$, where $a_0<b_0<\dots<a_m<0<b_m<\dots<a_n<b_n$ for some $0\leq m \leq n$. As $s\to +\infty$, we establish a general asymptotic formula up to and including the oscillatory term of order $1$, which involves a $θ$-functions-combination integral along a linear flow on an $n$-dimensional torus. If the linear flow has ``good Diophantine properties'' or the ergodic properties, we further improve the error estimate or the leading term for the asymptotics of the integral. These results can be combined for the case $n=1$, which lead to a precise large gap asymptotics up to an undetermined constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Confluent hypergeometric kernel determinant on multiple large intervals Xu, Taiyang Zhang, Lun Zhao, Zhengyang Mathematical Physics Classical Analysis and ODEs Probability 33C15, 41A60, 60B20, 60G55 The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig singular point for a broad class of unitary ensembles. It is the aim of this work to investigate large gap asymptotics of this process over a union of disjoint intervals $\cup_{j=0}^{n}(sa_j,sb_j)$, where $a_0<b_0<\dots<a_m<0<b_m<\dots<a_n<b_n$ for some $0\leq m \leq n$. As $s\to +\infty$, we establish a general asymptotic formula up to and including the oscillatory term of order $1$, which involves a $θ$-functions-combination integral along a linear flow on an $n$-dimensional torus. If the linear flow has ``good Diophantine properties'' or the ergodic properties, we further improve the error estimate or the leading term for the asymptotics of the integral. These results can be combined for the case $n=1$, which lead to a precise large gap asymptotics up to an undetermined constant. |
| title | Confluent hypergeometric kernel determinant on multiple large intervals |
| topic | Mathematical Physics Classical Analysis and ODEs Probability 33C15, 41A60, 60B20, 60G55 |
| url | https://arxiv.org/abs/2508.10463 |