Below is the ascii version of the abstract for 07-16.
The html version should be ready soon.
A random walk on the permutation group, some formal
long-time asymptotic relations
ABSTRACT. We consider the group of permutations of the vertices of a lattice. A
is generated by unit steps that each interchange two nearest neighbor
of the lattice. We study the heat equation on the permutation group,
Laplacian associated to the random walk. At t=0 we take as initial
a probability distribution concentrated at the identity. A natural
for the probability distribution at long times is that it is
'approximately' a product
of Gaussian distributions for each vertex. That is, each vertex
of the others. We obtain some formal asymptotic results in this
problem arises in certain ways of treating the Heisenberg model of
in statistical mechanics.