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
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
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