Annals of Applied Probability

Max $\kappa$-cut and the inhomogeneous Potts spin glass

Aukosh Jagannath, Justin Ko, and Subhabrata Sen

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Abstract

We study the asymptotic behavior of the Max $\kappa$-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi-type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 3 (2018), 1536-1572.

Dates
Received: March 2017
Revised: July 2017
First available in Project Euclid: 1 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1527840026

Digital Object Identifier
doi:10.1214/17-AAP1337

Mathematical Reviews number (MathSciNet)
MR3809471

Zentralblatt MATH identifier
06919732

Subjects
Primary: 90C27: Combinatorial optimization 82D30: Random media, disordered materials (including liquid crystals and spin glasses) 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G15: Gaussian processes 90C06: Large-scale problems

Keywords
MAX CUT spin glasses Potts model inhomogeneous random graphs

Citation

Jagannath, Aukosh; Ko, Justin; Sen, Subhabrata. Max $\kappa$-cut and the inhomogeneous Potts spin glass. Ann. Appl. Probab. 28 (2018), no. 3, 1536--1572. doi:10.1214/17-AAP1337. https://projecteuclid.org/euclid.aoap/1527840026


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