Work

Selberg integrals in 1D random Euclidean optimization problems

Year: 2019

Type: article

Abstract: We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points x and y is the Euclidean distance between them to an arbitrary power , the points are chosen at random with uniform measure. We derive the exact average cost for the random assignment problem, for any number of points using Selberg’s integrals. Some variants of these integrals enable the exact average cost for the bipartite travelling salesman problem to be derived.

Source: Journal of Statistical Mechanics Theory and Experiment

DOI: 10.1088/1742-5468/ab11d7

Authors: Sergio Caracciolo, Andrea Di Gioacchino, Enrico M Malatesta, Luca G Molinari

Institutions: University of Milan, Istituto Nazionale di Fisica Nucleare, Sezione di Milano

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W2892962770

FWCI: 1.145

Cites: 23

Cited by: 8

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