Amites Sarka

Western Washington University
, BH 217

Abstract

Coverage and Percolation

PlaceNpoints uniformly at random in a squareof areaN, whereNis a large number. Now imagine growinga disc around each point, at the same speed for every point.Initially, there will be isolated discs, and small clusters of discs,surrounded by a sea of empty space, but then, as the disc radiusrreaches about 0.6, a mysterious phenomenon known asperco-lationoccurs. Much later, asrreaches thecoverage threshold,the discs entirely cover the original square. Both the percola-tion and coverage thresholds, for this model and others, are ofinterest to physicists, chemists, biologists and engineers, as wellas mathematicians; come to the talk to find out why.