For more information about this meeting, contact Manfred Denker.
| Title: | Understanding Averages |
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| Seminar: | Seminar on Probability and its Application |
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| Speaker: | Michael Keane, Wesleyan University |
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| Abstract: |
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| 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 |
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| Date: | 04 / 01 / 2011 |
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| Time: | 02:20pm - 03:20pm |
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