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Extreme value theory for random walks on homogeneous spaces

Maxim Kirsebom
(University of Bristol)
Analysis Seminar
Thursday, 29 August, 2013, at 16:15-17:15, in Aud. D3 (1531-215)
For a random walk on a homogeneous space we are interested in the maximal excursions as well as the closest returns of the random walk. We study the distribution of these extreme events and in particular the limit of this distribution as the number of steps of the random walk tends to infinity. We consider this question for homogeneous spaces on which the averaging operator has spectral gap. 

In this talk we will discuss the key role that the spectral gap of the averaging operator plays in applying extreme value theory to random walks. This method yields various estimates on the limiting distributions of extreme events for random walks which in turn suffices to prove a logarithm law.
Contact person: Simon Kristensen