Technion, IEM faculty - Seminar in Probability and Stochastic Processes
 
Speaker: Gennady Samorodnitsky, Cornell University
 
Title: How do heavy tails express themselves in random environment: weak weak limit theorems
 
Date: 10/01/2012
 
Time: 11:30
 
Place: Hashmal-861
 
Abstract:  <http://ie.technion.ac.il/seminar_files/1324885848_S.txt>
 
Or read it here:
 
We consider a one-dimensional, transient random walk in a random
i.i.d. environment. The asymptotic behaviour of such
random walk depends to a large extent on a crucial parameter
kappa>0 that determines the fluctuations of the process.
When 0<kappa<2, the averaged distributions of the hitting times
of the random walk converge to a kappa-stable distribution. However,
it was shown recently that in this case there does not exist a
quenched limiting distribution of the hitting times. That is,
it is not true that for almost every fixed environment, the
distributions of the hitting times (centered and scaled in any manner)
converge to a non-degenerate distribution. We
show, however, that the quenched distributions do have a limit in the
weak sense. That is, the quenched distributions of the hitting times
 -- viewed as a random probability measure on R -- converge in
distribution to a random probability measure, which has interesting
stability properties.  Our results generalize both the averaged
limiting distribution and the non-existence of quenched limiting
distributions.
 
J. Peterson and G. Samorodnitsky
 
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