REAL

Atoms of the matching measure

Bencs, Ferenc and Mészáros, András (2022) Atoms of the matching measure. ELECTRONIC JOURNAL OF PROBABILITY, 27. ISSN 1083-6489

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Abstract

We prove that the matching measure of an infinite vertex-transitive connected graph has no atoms. Generalizing the results of Salez, we show that for an ergodic non-amenable unimodular random rooted graph with uniformly bounded degrees, the matching measure has only finitely many atoms. Ku and Chen proved the analogue of the Gallai-Edmonds structure theorem for non-zero roots of the matching polynomial for finite graphs. We extend their results for infinite graphs. We also show that the corresponding Gallai-Edmonds decomposition is compatible with the zero temperature monomer-dimer model.

Item Type: Article
Subjects: Q Science / természettudomány > QC Physics / fizika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 26 Jan 2024 10:28
Last Modified: 26 Jan 2024 10:28
URI: http://real.mtak.hu/id/eprint/186070

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