We study the problem of efficiently recovering the matching between anunlabelled collection of $n$ points in $\mathbb{R}^d$ and a small randomperturbation of those points . In this setting, the maximum likelihood estimator can be found in polynomial time as the solution of a linear assignmentproblem . We establish thresholds on $sigma^2 for the MLE to perfectly recover the planted matching (making no errors) and to strongly recover the planting matching . Our prooftechniques rely on careful analysis of the combinatorial structure of partialmatchings in large, weakly dependent random graphs using the first and secondmoment methods . These resultsextend to a recent line of work on recovering matchingsplanted in random graphs with independently-weighted edges

Author(s) : Dmitriy Kunisky, Jonathan Niles-Weed

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Keywords : matching - graphs - random - recover - points -

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