Correlation Decay for Maximum Weight Matchings on Sparse Graphs

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Lam, Wai-Kit, Sen, Arnab
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915820822593536
author Lam, Wai-Kit
Sen, Arnab
author_facet Lam, Wai-Kit
Sen, Arnab
contents We study correlation decay for the maximum weight matching problem on sparse graphs with i.i.d. edge weights. We show exponential decay of correlations when the underlying graphs are locally tree-like with uniformly bounded degree and the edge weights are exponential. We also prove a polynomial rate of decay of correlations for any finite graph with maximum degree at most three, again for exponential edge weights. As consequences of the correlation decay property, we obtain the existence of the maximum weight matching on infinite graphs, local weak convergence of the maximum weight matching, and a law of large numbers for its total weight.
format Preprint
id arxiv_https___arxiv_org_abs_2511_18861
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Correlation Decay for Maximum Weight Matchings on Sparse Graphs
Lam, Wai-Kit
Sen, Arnab
Probability
We study correlation decay for the maximum weight matching problem on sparse graphs with i.i.d. edge weights. We show exponential decay of correlations when the underlying graphs are locally tree-like with uniformly bounded degree and the edge weights are exponential. We also prove a polynomial rate of decay of correlations for any finite graph with maximum degree at most three, again for exponential edge weights. As consequences of the correlation decay property, we obtain the existence of the maximum weight matching on infinite graphs, local weak convergence of the maximum weight matching, and a law of large numbers for its total weight.
title Correlation Decay for Maximum Weight Matchings on Sparse Graphs
topic Probability
url https://arxiv.org/abs/2511.18861