Visiting assistant professor at the University of Rochester
Intersection Exponents for Random Walks on Cylinders
Abstract: Intersection exponents are a measure of how likely two random walks are to avoid each other. We show that intersection exponents for asymmetric random walks on d-dimensional half-infinite cylinders exist and 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.