Markov loops, determinants and Gaussian fields

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Yves Le Jan (LM-Orsay) This is my paper · ORCID

classification math.PR

keywords determinantsfieldsgaussianmarkovexplorelooploopsmeasures

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The purpose of this note is to explore some simple relations between loop measures, determinants, and Gaussian Markov fields.

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Loop clusters on complete graphs
math.PR 2025-04 conditional novelty 6.0 of 10

In the loop soup on the complete graph K_n, the number of clusters of size d converges to a mixed Poisson law with mixing variable exp(-dZ/κ), and clusters larger than n^{1-ε} appear almost surely.