The Alexander-Orbach conjecture holds in high dimensions

Details The Alexander-Orbach conjecture holds in high dimensions The Alexander-Orbach conjecture holds in high dimensions

2008-06-09

arxiv.org/abs/0806.1442v3

Mathematics

Probability

25 pages, 2 figures. To appear in Inventiones Mathematicae

Scientific paper

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.

Affiliated with

Also associated with

No associations

Rating

The Alexander-Orbach conjecture holds in high dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Alexander-Orbach conjecture holds in high dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Alexander-Orbach conjecture holds in high dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-400746