Superdiffusive behavior for a Brownian polymer in a Gaussian medium

Sergio De Carvalho Bezerra; Samy Tindel; Frederi Viens

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Superdiffusive behavior for a Brownian polymer in a Gaussian medium

Sergio De Carvalho Bezerra·Samy Tindel·Frederi Viens

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Abstract

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 $α<3/5$.

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Sergio De Carvalho Bezerra, Samy Tindel, Frederi Viens. 2007-09-12. Superdiffusive behavior for a Brownian polymer in a Gaussian medium. https://arxiv.org/abs/math/0603404

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