Niveau: Supérieur
Superdiffusivity for a Brownian polymer in a continuous Gaussian environment Sergio Bezerra ? Samy Tindel Institut Elie Cartan, Universite de Nancy 1 BP 239, 54506-Vandoeuvre-les-Nancy, France [bezerra,tindel]@iecn.u-nancy.fr Frederi Viens † Dept. Statistics & Dept. Mathematics, Purdue University 150 N. University St., West Lafayette, IN 47907-2067, USA March 1, 2007 Abstract This paper provides information about the asymptotic behavior of a one-dimen- sional Brownian polymer in random medium represented by a Gaussian field W on R+ ? R assumed to be 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 ? < 3/5. Key words and phrases: Polymer model, Random medium, Gaussian field, Free energy, Wandering exponent. MSC: 82D60, 60K37, 60G15. ?This author's research partially supported by CAPES. †This author's research partially supported by NSF grant no. : 0204999. 1
- wiener measure
- covariance function
- random environment
- gaussian field
- exponent ?
- any fixed
- fixed path
- dgxt
- potential