High-dimensional Gaussian fields with isotropic increments seen through spin glasses

Anton Klimovsky (EURANDOM, Eindhoven University of Technology)

Abstract


We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle point variational representation in terms of a Parisi-type functional for the free energy in the infinite-dimensional limit. The proofs are based on the techniques developed in the course of the rigorous analysis of the Sherrington-Kirkpatrick model with vector spins.

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Pages: 1-14

Publication Date: April 29, 2012

DOI: 10.1214/ECP.v17-1994

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