Title: Local vs. central limits of a chaotic walk in a frozen environment
Speaker: Lasse Leskelä
Aalto University
Time: Mon 27 Sep 2010 16:15-17:00
Place: Room U3322
TKK Main Building (Otakaari 1 M, Espoo)
(The talk is based on joint work with Mikko Stenlund, Courant Institute.)
Abstact:
We study particle propagation in a one-dimensional inhomogeneous medium where the dynamics are
generated by chaotic and deterministic local maps. For a uniformly distributed random initial
location, the particle's trajectory corresponds to a unidirectional random walk in an
inhomogeneous environment. We show that the random walk's probability mass function does not
converge to a Gaussian density, although the limiting distribution over a coarser diffusive space
scale is Gaussian. This result appears to be the first local limit theorem concerning random walks
in aperiodic nonrandom or quenched random environments, and among the first of its kind for
extended dynamical systems.