Einstein relation for biased random walk on Galton--Watson trees

Abstract

We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrary deep traps.

Minor errors corrected

References in corpus (2)

• Almost sure convergence for stochastically biased random walks on trees
• A central limit theorem for random walk in random environment on marked Galton-Watson trees

Cited by in corpus (4)

• Biased random walks on random graphs
• A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases
• 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
• Speed of the biased random walk on a Galton--Watson tree