A note on $\alpha$-permanent and loop soup
Probability
2023-07-06 v2 Combinatorics
Rings and Algebras
Abstract
In this paper, it is shown that -permanent in algebra is closely related to loop soup in probability. We give explicit expansions of -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.
Cite
@article{arxiv.2212.06095,
title = {A note on $\alpha$-permanent and loop soup},
author = {Xiaodan Li and Yushu Zheng},
journal= {arXiv preprint arXiv:2212.06095},
year = {2023}
}
Comments
9 pages, 1 figure; to appear in Electronic Communications in Probability