Superdiffusive behavior for a Brownian polymer in a Gaussian medium
Sérgio de Carvalho Bezerra, Samy Tindel, Frederi G Viens · arXiv (Cornell University) · 2006
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 $α<3/5$.