### DIMACS Special Seminar

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).