Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 17 (2012), paper no. 17, 14 pp.
High-dimensional Gaussian fields with isotropic increments seen through spin glasses
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.
Electron. Commun. Probab., Volume 17 (2012), paper no. 17, 14 pp.
Accepted: 29 April 2012
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 82D30: Random media, disordered materials (including liquid crystals and spin glasses) 60G15: Gaussian processes 60G60: Random fields 60F10: Large deviations
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Klimovsky, Anton. High-dimensional Gaussian fields with isotropic increments seen through spin glasses. Electron. Commun. Probab. 17 (2012), paper no. 17, 14 pp. doi:10.1214/ECP.v17-1994. https://projecteuclid.org/euclid.ecp/1465263150