On one property of Derrida–Ruelle cascades

Dmitry Panchenko; Michel Talagrand

doi:10.1016/j.crma.2007.10.035

Probability Theory

On one property of Derrida–Ruelle cascades

Presented by: Gilles Pisier

Dmitry Panchenko ¹; Michel Talagrand ²

¹ Texas A&M University, College Station, TX 77843, USA
² Équipe d'analyse de l'institut mathématique de Jussieu, 4, place Jussieu, 75230 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 653-656.

Abstract
Résumé

We present new results about Poisson–Dirichlet point processes and Derrida–Ruelle cascades that are motivated by applications to mean-field spin glass models and, in particular, by the attempt to express Guerra's interpolation in the Sherrington–Kirkpatrick model entirely in the language of the cascades.

Nous présentons une nouvelle propriété des processus ponctuels de Poisson–Dirichlet et des cascades de Derrida–Ruelle. Cela nous permet d'exprimer l'interpolation de Guerra dans le modèle de verres de spin de Sherrington–Kirkpatric entièrement dans le langage des cascades.

Received: 2007-09-25
Accepted: 2007-10-16
Published online: 2007-11-26

DOI: 10.1016/j.crma.2007.10.035

Author's affiliations:

Dmitry Panchenko ¹; Michel Talagrand ²

¹ Texas A&M University, College Station, TX 77843, USA
² Équipe d'analyse de l'institut mathématique de Jussieu, 4, place Jussieu, 75230 Paris cedex 05, France

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Dmitry Panchenko; Michel Talagrand. On one property of Derrida–Ruelle cascades. Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 653-656. doi : 10.1016/j.crma.2007.10.035. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.035/

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