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


 
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1. Title Title of document High-dimensional Gaussian fields with isotropic increments seen through spin glasses
 
2. Creator Author's name, affiliation, country Anton Klimovsky; EURANDOM, Eindhoven University of Technology; Netherlands
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian random fields; isotropic increments; random energy model; hierarchical replica symmetry breaking; Parisi Ansatz
 
3. Subject Subject classification 60K35; 82B44; 82D30; 60G15; 60G60; 60F10
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) European Commission (Marie Curie fellowship, project PIEF-GA-2009-251200); DFG and NWO (bilateral Dutch-German research group "Random Spatial Models from Physics and Biology"); Hausdorff Research Institute for Mathematics (Bonn)
 
7. Date (YYYY-MM-DD) 2012-04-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1994
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1994
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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