Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle

Abstract

We compute the two-point correlation function for spin configurations which are obtained by solving the Euclidean matching problem, for one family of points on a grid, and the second family chosen uniformly at random, when the cost depends on a power $p$ of the Euclidean distance. We provide the analytic solution in the thermodynamic limit, in a number of cases ($p>1$ open b.c.\ and $p=2$ periodic b.c., both at criticality), and analyse numerically other parts of the phase diagram.

arXiv comment34 pages, 10 figures

References in corpus (2)

• Scaling hypothesis for the Euclidean bipartite matching problem
• On the one dimensional Euclidean matching problem: exact solutions, correlation functions and universality

Cited by in corpus (16)

• Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions
• Quadratic stochastic Euclidean bipartite matching problem
• Random Euclidean matching problems in one dimension
• Solution for a bipartite Euclidean traveling-salesman problem in one dimension
• One-loop diagrams in the Random Euclidean Matching Problem
• Exact value for the average optimal cost of bipartite traveling-salesman and 2-factor problems in two dimensions
• The Dyck bound in the concave 1-dimensional random assignment model
• Finite-size corrections in the random assignment problem
• Random assignment problems on $2d$ manifolds
• Anomalous scaling of the optimal cost in the one-dimensional random assignment problem
• Criticality and conformality in the random dimer model
• Plastic number and possible optimal solutions for an Euclidean 2-matching in one dimension
• Selberg integrals in 1D random Euclidean optimization problems
• The p-Airy distribution
• Average optimal cost for the Euclidean TSP in one dimension
• The number of optimal matchings for Euclidean Assignment on the line