Intersection exponents for biased random walks on discrete cylinders

Abstract

We prove existence of intersection exponents xi(k,lambda) for biased random walks on d-dimensional half-infinite discrete cylinders, and show that, as functions of lambda, these exponents are real analytic. As part of the argument, we prove convergence to stationarity of a time-inhomogeneous Markov chain on half-infinite random paths. Furthermore, we show this convergence takes place at exponential rate, an estimate obtained via a coupling of weighted half-infinite paths.