Localization for a Random Walk in Slowly Decreasing Random Potential

Author(s)

Gallesco, Christophe ^[1] ; Popov, Serguei ^[1] ; Schuetz, Gunter M. ^[2]

Affiliation

^[1] Univ Campinas UNICAMP, Dept Stat, Inst Math Stat & Sci Computat, BR-13083859 Campinas, SP - Brazil

^[2] Forschungszentrum Julich, Inst Complex Syst, D-52425 Julich - Germany

• Document type: Journal article
• Source: Journal of Statistical Physics; v. 150, n. 2, p. 285-298, JAN 2013.
• Web of Science Citations: 1

Abstract

We consider a continuous time random walk X in a random environment on a{''}currency sign(+) such that its potential can be approximated by the function V:a{''}e(+)-> a{''}e given by where sigma W a Brownian motion with diffusion coefficient sigma > 0 and parameters b, alpha are such that b > 0 and 0 <alpha < 1/2. We show that P-a.s. (where P is the averaged law) with . In fact, we prove that by showing that there is a trap located around (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the ``pure{''} Sinai's regime, where the location of this trap is random on the scale ln(2) t. (AU)

• FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 11/21089-4 - Large deviation properties of the ASEP with random rates
• Grantee: Serguei Popov
• Support type: Research Grants - Visiting Researcher Grant - International