Tel Aviv University
Dear all,
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
Speaker: Oren Louidor, University of California, Los Angeles
Title: Trapping in the random conductance model.
Date: Monday, December 19
Time: 14:30
Place: Schreiber 309
We consider random walks on Z^d among nearest-neighbor random
conductances which are i.i.d., positive, bounded uniformly from above
but which can be arbitrarily close to zero. Our focus is on the
detailed properties of the paths of the random walk conditioned to
return back to the starting point after time 2n. We show that in the
situations when the heat kernel exhibits subdiffusive behavior ---
which is known to be possible in dimensions d ~I 4-- the walk gets
trapped for time of order n in a small spatial region. This proves
that the strategy used to infer subdiffusive lower bounds on the heat
kernel in earlier studies of this problem is in fact dominant. In
addition, we settle a conjecture on the maximal possible subdiffusive
decay in four dimensions and prove that anomalous decay is a tail and
thus zero-one event.
Joint work with Marek Biskup, Alexander Vandenberg and Alexander
Best regards,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>