Confluent hypergeometric kernel determinant on multiple large intervals

2025/08/14 by Xu, Taiyang, Zhang, Lun, Zhao, Zhengyang
#33C15 #41A60 #60B20 #60G55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.10463

Abstract

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 ∪_j=0ⁿ(sa_j,sb_j), where a₀

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