Random walks in random environment

• Grant number: 10/16085-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: November 16, 2010 - December 17, 2010
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Serguei Popov
• Grantee: Serguei Popov
• Visiting researcher: Nina Gantert
• Visiting researcher institution: University of Munster, Germany
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 09/52379-8 - Stochastic modeling of interacting systems, AP.TEM

Abstract

Recently, we obtained a law of large numbers for random walks on weighted (infinite supercritical) Galton-Watson trees. The rate of escape (the speed) is given in terms of effectiveconductances. In some particular cases, we proved that the speed is strictly smaller than the speed of simple random walk on Galton--Watson trees. The proof relies on finding a reversible measure for the environment seen from the particle. First, we want to extent these ideas to random unimodular networks and second, we want to use the stationary measure above to prove a Central Limit Theorem in the general setting. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GANTERT, NINA; MUELLER, SEBASTIAN; POPOV, SERGUEI; VACHKOVSKAIA, MARINA. Random walks on Galton-Watson trees with random conductances. Stochastic Processes and their Applications, v. 122, n. 4, p. 1652-1671, APR 2012. (10/16085-7, 09/08665-6)

GALLESCO, C.; GANTERT, N.; POPOV, S.; VACHKOVSKAIA, M.. A Conditional Quenched CLT for Random Walks Among Random Conductances on Z(d). Markov Processes and Related Fields, v. 20, n. 2, p. 287-328, 2014. (09/52379-8, 10/16085-7)