Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2015

Speaker:  James Propp, UMass Lowell
Title: A derandomized percolation explorer and a derandomized Polya urn model
Time: 2:30 PM, Monday, April 27, 2015
Place:  Malott 206

Abstract:I'll describe a derandomized variant of the percolation explorer process in an infinite wedge of hexagonal cells assigned states "plus" and "minus". Holroyd introduced this process a decade ago, inspired by the Cardy-Smirnov formula for percolation in a triangle. The derandomized process, extended to an infinite wedge, exhibits a form of self-organization in which at any given time the wedge is divided into distinct, slowly evolving "flow domains"; within each flow domain, successive particles flow along parallel exploration paths. We have made some progress toward analyzing the model by relating it to a derandomized version of the Polya urn model that replaces random propagation by rotor-routing. This is joint work with David Einstein and Alexander Holroyd.

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