Superdiffusive behavior for a Brownian polymer in a Gaussian medium

Sergio de Carvalho Bezerra (1) , Samy Tindel (1) , Frederi Viens (2)

1 IECN - Institut Élie Cartan de Nancy
2 Department of Statistics [West Lafayette]

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 $\alpha<3/5$.

Mots clés: Polymer model; Random medium; Gaussian field; Free energy; Wandering exponent

Domaines: Probabilités [math.PR]

Sergio de Carvalho Bezerra, Samy Tindel, Frederi Viens. Superdiffusive behavior for a Brownian polymer in a Gaussian medium. Annals of Probability, 2008, 222 (1), pp.000. ⟨10.48550/arXiv.math/0603404⟩. ⟨hal-00021047v2⟩