Localization and delocalization of random interfaces.
Velenik, Yvan (2006)
Probability Surveys [electronic only]
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Velenik, Yvan (2006)
Probability Surveys [electronic only]
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Caravenna, Francesco, Giacomin, Giambattista (2005)
Electronic Communications in Probability [electronic only]
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Erwin Bolthausen (2004-2005)
Séminaire Bourbaki
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The Parisi formula is an expression for the limiting free energy of the Sherrington-Kirkpatrick spin glass model, which had first been derived by Parisi using a non-rigorous replica method together with an hierarchical ansatz for the solution of the variational problem. It had become quickly clear that behind the solution, if correct, lies an interesting mathematical structure. The formula has recently been proved by Michel Talagrand based partly on earlier ideas and results by Francesco...
Toninelli, Fabio Lucio (2007)
Electronic Journal of Probability [electronic only]
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Picco, Pierre, Orlandi, Enza (2009)
Electronic Journal of Probability [electronic only]
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Michel Talagrand (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Atar, Rami, Athreya, Siva, Kang, Min (2001)
Electronic Communications in Probability [electronic only]
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Biskup, Marek, Prescott, Timothy M. (2007)
Electronic Journal of Probability [electronic only]
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Sakagawa, Hironobu (2009)
Electronic Journal of Probability [electronic only]
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Philippe Carmona (2010)
ESAIM: Probability and Statistics
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The sequence of random probability measures that gives a path of length , times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
Croydon, David A., Kumagai, Takashi (2008)
Electronic Journal of Probability [electronic only]
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