Recurrence and Diffusive Limits of Locally Perturbed Lorentz Processes
A locally perturbed Lorentz process is a Sinai billiard - a point particle moving freely and reflecting elastically among a periodic array of strictly convex scatterers - whose scatterer configuration has been altered inside a bounded region. Students learn how a probabilistic, random-walk-based method shows that such local perturbations leave the diffusive (Brownian) scaling limit and the almost-sure recurrence of the planar finite-horizon process unchanged, answering a 1981 question of Sinai, and see the still-open infinite-horizon analogue and companion open questions for random walks with unbounded jumps.
RANDOM WALKS AND LORENTZ PROCESSES DOMOKOS SZ ´ASZ Dedicated to the memory of P´al R´ev´esz
A survey (dedicated to Pal Revesz) of the recurrence and diffusive limit theory of Lorentz processes and their random-walk analogues. A Lorentz process is the billiard trajectory of a point particle …