High-dimensional Gaussian fields with isotropic increments seen through spin glasses
Probability
2014-02-11 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1108.5300,
title = {High-dimensional Gaussian fields with isotropic increments seen through spin glasses},
author = {Anton Klimovsky},
journal= {arXiv preprint arXiv:1108.5300},
year = {2014}
}
Comments
13 pages