Seminar series
Date
Mon, 16 May 2005
14:15
14:15
Location
DH 3rd floor SR
Speaker
Dr. Martin Barlow
Organisation
University of British Columbia
It is now known that the overall behaviour of a simple random walk (SRW) on
supercritical (p>p_c) percolation cluster in Z^d is similiar to that of the SRW
in Z^d. The critical case (p=p_c) is much harder, and one needs to define the
'incipient infinite cluster' (IIC). Alexander and Orbach conjectured in 1982
that the return probability for the SRW on the IIC after n steps decays like
n^{2/3} in any dimension. The easiest case is that of trees; this was studied by
Kesten in 1986, but we can now revisit this problem with new techniques.