Open Access
2023 A note on α-permanent and loop soup
Xiaodan Li, Yushu Zheng
Author Affiliations +
Electron. Commun. Probab. 28: 1-9 (2023). DOI: 10.1214/23-ECP530

Abstract

In this paper, it is shown that α-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of α-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.

Funding Statement

The first author is supported by the Fundamental Research Funds for the Central Universities. The second author is partially supported by NSFC, China (No. 11871162).

Citation

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Xiaodan Li. Yushu Zheng. "A note on α-permanent and loop soup." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP530

Information

Received: 14 December 2022; Accepted: 11 June 2023; Published: 2023
First available in Project Euclid: 4 July 2023

MathSciNet: MR4621590
zbMATH: 1519.15006
Digital Object Identifier: 10.1214/23-ECP530

Subjects:
Primary: 15A15 , 60G55 , 60G60

Keywords: loop soup , α-permanent

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