Superdiffusivity for a Brownian polymer in a continuous Gaussian environment

Sergio Bezerra Samy Tindel 1, 2 Frederi Viens
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field W on R+ × R which is white noise in time and functionvalued in space. According to the behavior of the spatial covariance of W, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any α <3/5.
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Submitted on : Wednesday, June 22, 2011 - 2:27:17 PM
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Sergio Bezerra, Samy Tindel, Frederi Viens. Superdiffusivity for a Brownian polymer in a continuous Gaussian environment. Annals of Probability, Institute of Mathematical Statistics, 2008, 36 (5), pp.1642-1675. ⟨10.1214/07-AOP363⟩. ⟨hal-00602426⟩



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