The Annals of Probability

Superdiffusivity for a Brownian polymer in a continuous Gaussian environment

Sérgio Bezerra, Samy Tindel, and Frederi Viens

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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 function-valued 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.

Article information

Ann. Probab. Volume 36, Number 5 (2008), 1642-1675.

First available in Project Euclid: 11 September 2008

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Mathematical Reviews number (MathSciNet)

Primary: 82D60: Polymers 60K37: Processes in random environments 60G15: Gaussian processes

Polymer model random medium Gaussian field free energy wandering exponent


Bezerra, Sérgio; Tindel, Samy; Viens, Frederi. Superdiffusivity for a Brownian polymer in a continuous Gaussian environment. Ann. Probab. 36 (2008), no. 5, 1642--1675. doi:10.1214/07-AOP363.

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