Limit theorems for multivariate Bessel processes in the freezing regime

Sergio Andraus and Michael Voit

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4771-4790

Abstract: Multivariate Bessel processes describe the stochastic dynamics of interacting particle systems of Calogero–Moser–Sutherland type and are related with β-Hermite and Laguerre ensembles. It was shown by Andraus, Katori, and Miyashita that for fixed starting points, these processes admit interesting limit laws when the multiplicities k tend to ∞, where in some cases the limits are described by the zeros of classical Hermite and Laguerre polynomials. In this paper we use SDEs to derive corresponding limit laws for starting points of the form k⋅x for k→∞ with x in the interior of the corresponding Weyl chambers. Our limit results are a.s. locally uniform in time. Moreover, in some cases we present associated central limit theorems.

Keywords: Interacting particle systems; Calogero–Moser–Sutherland models; Strong limiting laws; Central limit theorems; Zeros of Hermite polynomials; Zeros of Laguerre polynomials; Hermite ensembles; Laguerre ensembles (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:11:p:4771-4790

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DOI: 10.1016/j.spa.2018.12.011

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