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On differentiability of the Parisi formula


 
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1. Title Title of document On differentiability of the Parisi formula
 
2. Creator Author's name, affiliation, country Dmitry Panchenko; Texas A&M University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Sherrington-Kirkpatrick model, Parisi formula.
 
3. Subject Subject classification 60K35, 82B44
 
4. Description Abstract It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2008-05-04
 
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/1365
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1365
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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