- Series
- Stochastics Seminar
- Time
- Thursday, February 16, 2012 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Oren Louidor – UCLA
- Organizer
- Karim Lounici
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 \geq 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
Rozinov.