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The Continuum Directed Random Polymer

Alberts, Tom and Khanin, Konstantin and Quastel, Jeremy (2014) The Continuum Directed Random Polymer. Journal of Statistical Physics, 154 (1-2). pp. 305-326. ISSN 0022-4715.

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Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter β, and for a given β and realization of the noise the path is a Markov process. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all β>0 and for almost all realizations of the white noise the path measure has the same Hölder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).

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Additional Information:© 2013 Springer Science+Business Media New York. Received: 2 June 2013; Accepted: 12 October 2013; Published online: 31 October 2013. Research of all three authors supported by the Natural Sciences and Engineering Research Council of Canada.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Directed random polymers, KPZ
Issue or Number:1-2
Record Number:CaltechAUTHORS:20131112-112055680
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Official Citation: The Continuum Directed Random Polymer Tom Alberts, Konstantin Khanin, Jeremy Quastel Pages 305-326
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:42382
Deposited By: David McCaslin
Deposited On:13 Nov 2013 17:16
Last Modified:03 Oct 2019 05:58

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