Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions

Michael Voit and Jeannette H.C. Woerner

Stochastic Processes and their Applications, 2022, vol. 143, issue C, 207-253

Abstract: We study Bessel and Dunkl processes (Xt,k)t≥0 on RN with possibly multivariate coupling constants k≥0. These processes describe interacting particle systems of Calogero–Moser–Sutherland type with N particles. For the root systems AN−1 and BN these Bessel processes are related with β-Hermite and β-Laguerre ensembles. Moreover, for the frozen case k=∞, these processes degenerate to deterministic or pure jump processes.

Keywords: Dunkl-Bessel processes; Calogero–Moser–Sutherland models; β-ensembles; Semicircle laws; Marchenko–Pastur laws; Free convolution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.10.005

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