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

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  • Voit, Michael
  • Woerner, Jeannette H.C.

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.

Suggested Citation

  • Voit, Michael & Woerner, Jeannette H.C., 2022. "Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 207-253.
  • Handle: RePEc:eee:spapps:v:143:y:2022:i:c:p:207-253
    DOI: 10.1016/j.spa.2021.10.005
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    References listed on IDEAS

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    1. Andraus, Sergio & Voit, Michael, 2019. "Limit theorems for multivariate Bessel processes in the freezing regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4771-4790.
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