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On Ruelle's probability cascades and an abstract cavity method


Bolthausen, E; Sznitman, A S (1998). On Ruelle's probability cascades and an abstract cavity method. Communications in Mathematical Physics, 197(2):247-276.

Abstract

We construct in this work a Markov process which describes a clustering mechanism through which equivalence classes on ¾ are progressively lumped together. This clustering process gives a new description of Ruelle's continuous probability cascades. It also enables to introduce an abstract cavity method, which mimicks certain features of the cavity method developed by physicists in the context of the Sherrington Kirkpatrick model.

Abstract

We construct in this work a Markov process which describes a clustering mechanism through which equivalence classes on ¾ are progressively lumped together. This clustering process gives a new description of Ruelle's continuous probability cascades. It also enables to introduce an abstract cavity method, which mimicks certain features of the cavity method developed by physicists in the context of the Sherrington Kirkpatrick model.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:clustering process; Ruelle's probability cascades; cavity method
Language:English
Date:1998
Deposited On:30 Apr 2010 08:44
Last Modified:20 Feb 2018 08:04
Publisher:Springer
ISSN:0010-3616
Additional Information:The original publication is available at www.springerlink.com
OA Status:Closed
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s002200050450
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1652734
http://www.zentralblatt-math.org/NEW/zmath/search/?q=an%3A0927.60071
http://www.math.ucla.edu/~prob-mp/archived_classes/285k.1.06s/related/Bolthausen-Sznitman-CMP98.pdf (Author)

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