Superdiffusive behavior for a Brownian polymer in a Gaussian medium

Details Superdiffusive behavior for a Brownian polymer in a Gaussian medium Superdiffusive behavior for a Brownian polymer in a Gaussian medium

2006-03-16

arxiv.org/abs/math/0603404v2

Annals of Probability 222, 1 (2008) 000

Mathematics

Probability

31 pages; accepted for publication in Annals of Probability; Revised version of "Some scaling limits for a brownian polymer in

Scientific paper

This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a space-time Gaussian field W assumed to be white noise in time and function-valued in space. According to the behavior of the spatial covariance 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 $\alpha<3/5$.

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