Avril 11, 2013
Product-form Invariant Measures for Brownian Motion with Drift
Satisfying a Skew-symmetry Type Condition
Janosch Ortmann, University of Toronto
Motivated by recent developments on positive-temperature
polymer models we propose a generalisation of reflected Brownian motion
(RBM) in a polyhedral domain. Our process is obtained by replacing the
singular drift on the boundary by a continuous one which depends, via a
potential U, on the position of the process relative to the domain. We
show that our generalised process has an invariant measure in product
form, under a certain skew-symmetry condition that is independent of the
choice of potential. Applications include TASEP-like particle systems,
generalisations of Brownian motion with rank-dependent drift and
diffusions connected to the generalised Pitman transform.
The talk is based on joint work with Neil O'Connell.