Max ?-cut and the inhomogeneous Potts spin glass

We study the asymptotic behavior of the Max κ-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...

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Bibliographic Details
Published in:The Annals of applied probability 2018-06, Vol.28 (3), p.1536
Main Authors: Jagannath, Aukosh, Ko, Justin, Sen, Subhabrata
Format: Article
Language:English
Subjects:
Asymptotic properties
Constraint modelling
Free energy
Graph theory
Ground state
Melt spinning
Probability
Spin glasses
Temperature
Online Access:Get full text
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Summary:We study the asymptotic behavior of the Max κ-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.
ISSN:1050-5164
2168-8737
DOI:10.1214/17-AAP1337