Freezing Limits for Beta-Cauchy Ensembles

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-05-17 DOI:10.3842/SIGMA.2022.069
M. Voit
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引用次数: 2

Abstract

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 $\beta$-Hermite and Laguerre ensembles. In this paper we study corresponding Cauchy processes constructed via some subordination. This leads to $\beta$-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 $\beta$-Hermite and Laguerre ensembles and for Bessel processes.
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β -柯西系综的冻结极限
与根系统$A_{N-1}$和$B_N$相关的贝塞尔过程描述了在$\mathbb R$上与$N$粒子相互作用的粒子系统;它们形成了经典的hermite和Laguerre合奏的动态版本。本文研究了相应的由隶属关系构造的柯西过程。这导致了在显式分布的两种情况下的$\beta$-Cauchy集成。对于这些分布,我们在冻结状态下,即当参数趋于无穷时,导出了固定N的中心极限定理。结果与已知的$\beta$-Hermite和Laguerre系综和贝塞尔过程的冻结结果密切相关。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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