Biased random walks on random graphs

Abstract

These notes cover one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. The aim is to review recent mathematical developments in the field of random walks in random environment. Our main focus will be on directionally transient and reversible random walks on different types of underlying graph structures, such as $\mathbb{Z}$, trees and ${\mathbb{Z}}^d$ for $d\ge 2$.

Survey based one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. 64 pages, 16 figures

References in corpus (6)

• Quenched invariance principle for simple random walk on percolation clusters
• The Alexander-Orbach conjecture holds in high dimensions
• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• Ageing in the parabolic Anderson model
• The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias
• Einstein relation for biased random walk on Galton--Watson trees

Cited by in corpus (9)

• Scaling limit for the ant in a simple labyrinth
• Non-Gaussian fluctuations of randomly trapped random walks
• The tail of the length of an excursion in a trap of random size
• Negative mobility, sliding and delocalization for stochastic networks
• Differentiability of the speed of biased random walks on Galton-Watson trees
• Biased random walk on the trace of biased random walk on the trace of...
• Central limit theorems for biased randomly trapped random walks on Z
• Favorite sites of randomly biased walks on a supercritical Galton-Watson tree
• The speed of a biased random walk on a Galton-Watson tree is analytic