Random overlap structures: properties and applications to SPIN glasses
type: Item
instance of: scholarly article
title: Random overlap structures: properties and applications to SPIN glasses
zbMATH Open document ID: 1275.82005
author: Louis-Pierre Arguin
author: Sourav Chatterjee
publication date: 2013-06-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.1823
review text: The authors consider some connections between random probability measures on Hilbert spaces and the Gibbs measures of spin glasses with Gausian disorder. Random overlap structures are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. It is proved that the so-called ``cavity mapping'' on the space of random overlap structures is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spin glass models.
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 6176809
zbMATH Keywords: probability measures on Hilbert spaces
zbMATH Keywords: spin glasses
zbMATH Keywords: stochastic stability
zbMATH Keywords: ultrametricity
zbMATH Keywords: Parisi formula
reviewed by: Nasir N. Ganikhodjaev
MaRDI profile type: Publication
OpenAlex ID: W2125399341
arXiv ID: 1011.1823
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DOI: 10.1007/S00440-012-0431-6
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article