冻结状态下与Calogero-Moser-Sutherland粒子模型相关的微分方程

IF 0.6 4区 数学 Q3 MATHEMATICS
M. Voit, Jeannette H. C. Woerner
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引用次数: 8

摘要

多元贝塞尔过程描述了Calogero-Moser-Sutherland粒子模型,并与$\beta$ -Hermite和$\beta$ -Laguerre系综有关。它们依赖于根系统和多样性$k$。最近,推导了$k\to\infty$的几个极限定理,其中极限取决于这些冻结状态下相关ode的解。本文研究了一类在其域边界上奇异的微分方程的解。特别地,我们证明了对于任意边界点的起始点,对于$t>0$, ode在其定义域内总是承认唯一解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime
Multivariate Bessel processes describe Calogero-Moser-Sutherland particle models and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity $k$. Recently, several limit theorems for $k\to\infty$ were derived where the limits depend on the solutions of associated ODEs in these freezing regimes. In this paper we study the solutions of these ODEs which are are singular on the boundaries of their domains. In particular we prove that for a start in arbitrary boundary points, the ODEs always admit unique solutions in their domains for $t>0$.
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The main purpose of Hokkaido Mathematical Journal is to promote research activities in pure and applied mathematics by publishing original research papers. Selection for publication is on the basis of reports from specialist referees commissioned by the editors.
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