RENORMALIZATION GROUPS AND CENTRAL LIMIT THEOREMS IN PERCOLATION
 
 
DR. MARTIN BAZANT
Department of Mathematics
Massachusetts Institute of Technology


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.)
 

MONDAY, SEPTEMBER 27, 1999
4:15 PM
Building 2, Room 105
Refreshments will be served at 3:45 PM in Building 2, Room 349


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