A connection between MAX $\kappa$-CUT and the inhomogeneous Potts spin glass in the large degree limit

Aukosh Jagannath; Justin Ko; Subhabrata Sen

doi:10.1214/17-aap1337

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arXiv · 1703.03455

A connection between MAX $\kappa$-CUT and the inhomogeneous Potts spin glass in the large degree limit

Aukosh Jagannath·Justin Ko·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.

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Aukosh Jagannath, Justin Ko, Subhabrata Sen. 2017-03-09. A connection between MAX $\kappa$-CUT and the inhomogeneous Potts spin glass in the large degree limit. https://doi.org/10.1214/17-aap1337

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