Superdiffusivity for a Brownian polymer in a continuous Gaussian environment Sergio Bezerra Samy Tindel
33 pages
English

Superdiffusivity for a Brownian polymer in a continuous Gaussian environment Sergio Bezerra Samy Tindel

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33 pages
English
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Description

Niveau: Supérieur

  • dissertation


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


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Publié par
Nombre de lectures 11
Langue English

Extrait

Superdiusivity for a Brownian polymer in Gaussian environment
S io BezerraSamy Tindel erg InstitutElieCartan,UniversitedeNancy1 BP239,54506-Vandoeuvre-les-Nancy,France [bezerra,tindel]@iecn.u-nancy.fr
a
Frederi ViensDept. Statistics & Dept. Mathematics, Purdue University 150 N. University St., West Lafayette, IN 47907-2067, USA viens@purdue.edu
March 1, 2007
Abstract
continuous
This paper provides information about the asymptotic behavior of a one-dimen-sional Brownian polymer in random medium represented by a Gaussian eldWon R+Rassumed to be white noise in time and function-valued in space. According to the behavior of the spatial covariance ofW, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to innity: the polymer is proved to be superdiusive, with a wandering exponent exceeding any  <3/5.
Key words and phrases:Polymer model, Random medium, Gaussian eld, Free energy, Wandering exponent.
MSC:82D60, 60K37, 60G15. This author’s research partially supported by CAPES.  : 0204999.This author’s research partially supported by NSF grant no.
1
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