论文标题
Beta-Cauchy合奏的冻结极限
Freezing Limits for Beta-Cauchy Ensembles
论文作者
论文摘要
Bessel过程与root Systems $ a_ {n-1} $和$ b_n $相关联，描述了与$ \ Mathbb r $上的$ n $粒子的交互粒子系统；它们形成了经典的$β$ - 赫米特和拉瓜合奏的动态版本。在本文中，我们研究了通过某些从属构建的相应的库奇过程。在这两种情况下，这都会导致$β$ -Cauchy合奏。对于这些分布，我们在冻结体制中的固定$ n $得出中心限制定理，即当参数趋于无穷大时。该结果与$β$ -HERMITE和LAGUERRE集团以及Bessel过程的相应已知冻结结果密切相关。
Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $β$-Hermite and Laguerre ensembles. In this paper we study corresponding Cauchy processes constructed via some subordination. This leads to $β$-Cauchy ensembles in both cases with explicit distributions. For these distributions we derive central limit theorems for fixed $N$ in the freezing regime, i.e., when the parameters tend to infinity. The results are closely related to corresponding known freezing results for $β$-Hermite and Laguerre ensembles and for Bessel processes.
