Motion by mean curvature and Dyson Brownian Motion

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-10-20 DOI:10.1214/23-ecp540

Ching-Peng Huang, D. Inauen, Govind Menon

引用次数: 4

Abstract

We construct Dyson Brownian motion for $\beta \in (0,\infty]$ by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within the space of Hermitian matrices. When $\beta$ is infinite, the eigenvalues evolve by Coulombic repulsion and the group orbits evolve by motion by (minus one half times) mean curvature.

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平均曲率运动与戴森布朗运动

将黎曼流形上布朗运动的外在构造适应于厄米矩阵空间内群轨道的几何构造，构造了$\beta \in (0,\infty]$的戴森布朗运动。当$\beta$为无穷大时，特征值通过库仑斥力演化，群轨道通过(- 1 / 2)平均曲率的运动演化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.