A random walk on the permutation group, some formal long-time asymptotic relations

Details A random walk on the permutation group, some formal long-time asymptotic relations A random walk on the permutation group, some formal long-time asymptotic relations

2007-01-17

arxiv.org/abs/math-ph/0701049v1

Physics

Mathematical Physics

16 pages

Scientific paper

We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the Laplacian associated to the random walk. At t=0 we take as initial conditions a probability distribution concentrated at the identity. A natural conjecture for the probability distribution at long times is that it is 'approximately' a product of Gaussian distributions for each vertex. That is, each vertex diffuses independently of the others. We obtain some formal asymptotic results in this direction. The problem arises in certain ways of treating the Heisenberg model of ferromagnetism in statistical mechanics.

Affiliated with

Also associated with

No associations

Rating

A random walk on the permutation group, some formal long-time asymptotic relations 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 A random walk on the permutation group, some formal long-time asymptotic relations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A random walk on the permutation group, some formal long-time asymptotic relations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-120501