Electronic Communications in Probability

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

Anton Klimovsky

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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.

Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 17, 14 pp.

Dates
Accepted: 29 April 2012
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263150

Digital Object Identifier
doi:10.1214/ECP.v17-1994

Mathematical Reviews number (MathSciNet)
MR2915663

Zentralblatt MATH identifier
06049248

Subjects
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

Keywords
Gaussian random fields isotropic increments random energy model hierarchical replica symmetry breaking Parisi Ansatz

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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References

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