RENORMALIZATION GROUPS AND CENTRAL LIMIT THEOREMS IN PERCOLATION

DR. MARTIN BAZANTMassachusetts Institute of Technology

Department of Mathematics

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 pc. The "order
parameter" for the phase transition is the size S of the largest cluster
as : For p <pc it is typically "small", S=O(log N), while for
p>pc 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 FN(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.)

Refreshments will be served at 3:45 PM in Building 2, Room 349MONDAY, SEPTEMBER 27, 1999

4:15 PM

Building 2, Room 105

Applied Math Colloquium: http://www-math.mit.edu/amc/fall99

Math Department: http://www-math.mit.edu