On the structure of quasi-stationary competing particle systems

Annals of Probability

Volumn 37, Issue 3, 2009, Pages 1080-1113

  Arguin, Louis Pierre ^a   Aizenman, Michael ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Point processes; Quasi stationarity; Ruelle probability cascades; Spin glasses; Ultrametricity

Indexed keywords

EID: 77249140657     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOP429     Document Type: Article

References (19)

1. AIZENMAN, M., SIMS, R. and STARR, S. L. (2003). An extended variational principle for the SK spin-glass model. Phys. Rev. B 68 214403
2. AIZENMAN, M., SIMS, R. and STARR, S. L. (2007). Mean-field spin glass models from the cavity-ROSt perspective. In Prospects in Mathematical Physics. Contemporary Mathematicians 437 1-30. Amer. Math. Soc., Providence, RI
3. ALDOUS, D. J. (1985). Exchangeability and related topics. In École d'étéde Probabilités de Saint-Flour, XIII-1983. Lecture Notes in Math. 1117 1-198. Springer, Berlin
4. ARGUIN, L.-P. (2007). Spin glass computations and Ruelle's probability cascades. J. Stat. Phys. 126 951-976
5. ARGUIN, L.-P. (2007). A dynamical characterization of Poisson-Dirichlet distributions. Electron. Comm. Probab. 12 283-290 (electronic)
6. ARGUIN, L.-P. (2008). Competing particle systems and the Ghirlanda-Guerra identities. Electron. J. Probab. 13 2101-2117
7. BERTOIN, J. (2006). Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics 102 288. Cambridge Univ. Press, Cambridge
8. BOLTHAUSEN, E. and SZNITMAN, A.-S. (1998). On Ruelle's probability cascades and an abstract cavity method. Comm. Math. Phys. 197 247-276
9. DERRIDA, B. (1985). A generalization of the random energy model which includes correlations between energies. J. Phys. Lett. 46 L401-L407
10. DOVBYSH, L. N. and SUDAKOV, V. N. (1982). Gram-de Finetti matrices. J. Soviet. Math. 24 3047-3054
11. GUERRA, F. (2003). About the cavity fields in mean field spin glass models. Preprint. Available at arxiv: cond-mat/0307673.
12. GUERRA, F. (2003). Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys. 233 1-12
13. HESTIR, K. (1989). A representation theorem applied to weakly exchangeable nonnegative definite arrays. J. Math. Anal. Appl. 142 390-402
14. HORN, R. A. and JOHNSON, C. R. (1985). Matrix Analysis. Cambridge Univ. Press, Cambridge.
15. MÉZARD, M., PARISI, G. and VIRASORO, M. A. (1987). Spin Glass Theory and Beyond. World Scientific Lecture Notes in Physics 9. World Scientific, Teaneck, NJ.
16. RUELLE, D. (1987). A mathematical reformulation of Derrida's REM and GREM. Comm. Math. Phys. 108 225-239
17. RUZMAIKINA, A. and AIZENMAN, M. (2005). Characterization of invariant measures at the leading edge for competing particle systems. Ann. Probab. 33 82-113
18. SIMON, B. (1993). The Statistical Mechanics of Lattice Gases, Vol. I. Princeton Univ. Press, Princeton, NJ.
19. TALAGRAND, M. (2006). The Parisi formula. Ann. Math. (2) 163 221-263