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Annales de l’Institut Henri Poincaré D


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Volume 8, Issue 1, 2021, pp. 35–88
DOI: 10.4171/AIHPD/97

Published online: 2020-12-12

On the unbalanced cut problem and the generalized Sherrington–Kirkpatrick model

Aukosh Jagannath[1] and Subhabrata Sen[2]

(1) University of Waterloo, Canada
(2) Harvard University, Cambridge, USA

We establish a strict asymptotic inequality between a class of graph partition problems on the sparse Erdős–Rényi and random regular graph ensembles with the same average degree. Along the way, we establish a variational representation for the ground state energy for generalized mixed $p$-spin glasses and derive strict comparison inequalities for such models as the alphabet changes.

Keywords: Random graphs, unbalanced cuts, spin glasses, gamma convergence

Jagannath Aukosh, Sen Subhabrata: On the unbalanced cut problem and the generalized Sherrington–Kirkpatrick model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), 35-88. doi: 10.4171/AIHPD/97