Applied Mathematics Colloquium, MIT
Monday, September 27, 1999
4:15pm, Room 2-105
Title: Renormalization Groups and Central Limit Theorems in Percolation
Speaker: Dr. Martin Bazant
Department of Mathematics, MIT
Abstract:
Percolation is a simple model for spatial disorder, which amounts to
randomly coloring each of N sites in a periodic lattice either black
or white with probability p and then identifying "clusters" of
adjacent black sites. Percolation is a cornerstone of statistical
physics because it displays a "phase transition" with critical point
p_c. The "order parameter" for the phase transition is the size S of
the largest cluster as N -> oo: For p < p_c it is typically "small",
S = O(log N), while for p > p_c it is "large", S = O(N). In this
talk, mathematical analysis and computer simulations are presented for
the finite-size scaling of the probability distribution F_N(S), and
connections are revealed between renormalization group methods in
physics and the limit theorems of probability theory.
(No knowledge of physics is assumed, only basic probability.)