Freezing Limits for Beta-Cauchy Ensembles - Voit, Michael (Symmetry, Integrability and Geometry: Methods and Applications, 2022)
Bessel processes associated with the root systems ₋₁ and describe interacting particle systems with particles on ℝ; they form dynamic versions of the classical -Hermite and Laguerre ensembles. In this paper, we study corresponding Cauchy processes constructed via some subordination. This leads to -Cauchy ensembles in both cases with explicit distributions. For these distributions, we derive central limit theorems for fixed in the freezing regime, i.e., when the parameters tend to infinity. The results are closely related to corresponding known freezing results for -Hermite and Laguerre ensembles and for Bessel processes.