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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.