Random walk in an external random potential and applications to aging in disordered spin systems

• Grant number: 13/12645-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 11, 2014
• End date: April 06, 2014
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Christophe Frédéric Gallesco
• Grantee: Christophe Frédéric Gallesco
• Visiting researcher: Gunter Markus Schutz
• Visiting researcher institution: Forschungszentrum Jülich, Germany
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

We study the behaviour of null-recurrent random walks on $\Z^+$ with a local drift that decays asymptotically in the distance $k$ from the origin with a power law with exponent $\alpha$ and an amplitude $b_k$. For the same models we investigate the meeting probabilities of independent random walks and use duality to apply these results to study aging in the Glauber-Isingspin relaxation dynamics. (AU)