Title: The Combinatorics of Coordinate Percolation
Speaker: Lizz Moseman, Dartmouth College
Date: Friday, March 30, 2007 3:00pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
In coordinate percolation on an (n) dimensional lattice with threshold (1{+}t), random variables (a_i(k)) are assigned to each (1 ≤ i ≤ n) and (k ge 0). A point (v = (v_1, ldots,v_n)) is open if (a_1(v_1) + a_2(v_2) + cdots +a_n(v_n) < 1+t) and closed otherwise. What is the probability that the origin is in an infinite open cluster? Various combinatorial methods are used, including algorithms and stochastic processes, to answer this question for the case (n=2) and offer progress when (n>2).