abstract:
Lecture 3: Convergence results: Comparative studies
I will compare the consequences of the different convergence criteria for a number of systems, among them:
(a) systems with finite-coordination exclusions;
(b) polymer or contour systems;
(c) zeros of chromatic polynomials, and
(d) the hard-sphere gas.
additional material:
The slides of Roberto Fernández'
first
(Feb 8) and second
(Mar 4) lecture (1MB each).
abstract:
We consider a supercritical Galton-Watson
tree, conditioned on survival (in particular, this includes the case of the
infinite percolation cluster of a regular tree) and run a biased random walk
on this tree.
We investigate the distribution of the walker at time n and possible limit
laws.
Joint work (in progress)
with Gerard Ben Arous, Alexander Fribergh and Alan Hammond.