The local central limit theorem and some applications
speaker: Peter Nandori (University of Maryland)abstract: We present a convenient joint generalization of mixing and the local version of the central limit theorem (MLLT) for probability preserving dynamical systems. We verify that the MLLT holds for several examples of hyperbolic systems by reviewing old results for maps and presenting new results for flows. Then we discuss two applications in infinite ergodic theory. First, we prove the mixing of global observables by some infinite measure preserving hyperbolic systems that are well approximated by periodic systems (examples include billiards with small potential field and various ping pong models). Here, global observables are functions that are not integrable with respect to the infinite invariant measure, but have convergent average values over large boxes. Second, we discuss the Birkhoff theorem for such global observables in the simplest case: iid random walks. The talk is based on joint work with Dmitry Dolgopyat and in parts with Marco Lenci.
timetable:
Tue 4 Jun, 16:20 - 17:05, Aula Dini
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