PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Manfred Denker.

Title:Understanding Averages
Seminar:Seminar on Probability and its Application
Speaker:Michael Keane, Wesleyan University
Abstract:
Sequences of real numbers for which the differences of successive terms tend to zero (quasi-Cauchy sequences) need not be convergent. Examples usually given have an artificial flavor. We present two examples known to us which seem to arise naturally. In the situation in which such a sequence arises as a dynamical average, many classical questions of this existence remain puzzlingly unresolved. We discuss the possibility of exhibition of simple nonconvergent sequences, with partial success. The lecture then continues with a simple proof of the ergodic theorem, based on 30 year old ideas of Kamae and Shields, and an extension due to Katznelson and Weiss to the subadditive domain. We then give an application showing exponential convergence of approximation of pairs of irrational numbers using the modified Jacobi-Perron algorithm (joint work with Fujita, Ito, and Ohtsuki), and discuss proofs of multidimensional ergodic theorems using our method.

Room Reservation Information

Room Number:MB106
Date:04 / 01 / 2011
Time:02:20pm - 03:20pm