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Neighborhood growth dynamics on the Hamming plane

Mathematical Physics & Probability

Speaker: Janko Gravner, UC Davis
Location: 1147 MSB
Start time: Wed, Oct 5 2016, 4:30PM

This talk will be a long range growth model on the two-dimensional lattice. The decision to add a point is made by counting the currently occupied points
on the entire horizontal and the entire vertical line through it, and checking
whether the pair of counts lies outside a fixed Young diagram. We focus on two related extremal quantities. The first is the size of the smallest set that
eventually occupies the entire plane. The second is the minimum of an energy-entropy functional that comes from the scaling of the probability of eventual full occupation versus the density of the initial product measure within a rectangle. The main results are on the existence of this scaling and the behavior of these quantities for large Young diagrams. This is joint work with David Sivakoff and Erik Slivken.