关于α-永久和环状汤的一个注记

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-12-12 DOI:10.1214/23-ECP530

Xiaodan Li, Yushu Zheng

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引用次数: 0

摘要

本文证明了代数中的$\ α $-permanent与概率中的环汤密切相关。本文给出了块矩阵的$\ α $-永久元的显式展开式，该展开式是由$*$-森林相关的矩阵得到的，$*$-森林是一类特殊的包含三对角矩阵的矩阵。它的证明有两种方式，一种是直接组合证明，另一种是通过环汤的概率证明。

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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A note on α-permanent and loop soup

In this paper, it is shown that $\alpha$-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of $\alpha$-permanents of the block matrices obtained from matrices associated to $*$-forests, which are a special class of matrices containing tridiagonal matrices. It is proved in two ways, one is the direct combinatorial proof, and the other is the probabilistic proof via loop soup.

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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.