On the gap probability of the tacnode process

Autor:	Yao, Luming, Zhang, Lun
Rok vydání:	2023
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Probability 33C15 60B20 60K35
Druh dokumentu:	Working Paper
Popis:	The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap probability of the thinned/unthinned tacnode process over $(-s,s)$. We establish an integral representation of the gap probability in terms of the Hamiltonian associated with a system of differential equations. With the aids of some remarkable differential identities for the Hamiltonian, we also compute large gap asymptotics, up to and including the constant term in the thinned case. As direct applications, we obtain expectation, variance and a central limit theorem for the associated counting function. Comment: 73 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.05622 Zobrazit plný text záznamu View this record from Arxiv