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Discrete Math

Diffusion on Graphs

Bhargav Narayanan, Rutgers University

Location:  HILL 705
Date & time: Monday, 11 September 2017 at 2:00PM - 3:00PM

Abstract:  Diffusion on a graph G is a cellular automaton describing how integer labels on the vertices of G evolve. We view the label of a vertex as the number of chips at that vertex, and at each step, each vertex simultaneously sends one chip to each of its neighbours with fewer chips. What can we say about the trajectories of various initial configurations in this process? Here’s an amuse bouche: this firing rule may generate negative labels when started from a completely positive initial configuration, so it is not clear, a priori, if one must even have periodic behaviour necessarily!

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