Rates of diffusion in dynamical systems with random jumps.

摘要

This dissertation explores the diffusion properties of a large class of measures under a dynamical system on ⋃i=0infinity S1i with randomly occurring jumps that behave according to a particular probability distribution. The drift rate for the center of mass of the system is then defined and is shown to be well defined Lebesgue almost everywhere. Properties of the drift rate are then explored. In particular the drift rate is shown to be continuous as a function of the probability "jump" distribution and, in a special case, it is shown that the drift rate increases with the probability of jumping. Finally, a central limit theorem for fluctuations about the drift rate is proved. The results are obtained by modeling the system as a random map on a compact space, and using the ergodic properties of the random map.