Markov Chains and Emergent Behavior

02/02/2018 - 4:15pm
02/02/2018 - 5:15pm
Sarah Cannon

Studying random samples drawn from large, complex sets is one way to begin to learn about typical properties and behaviors. However, it is important that the samples examined are random enough: studying samples that are unexpectedly correlated or drawn from the wrong distribution can produce misleading conclusions. Sampling processes using Markov chains have been utilized in physics, chemistry, and computer science, among other fields, but they are often used without careful analysis of their reliability. Mathematically guaranteeing that widely-used Markov chain sampling processes produce reliably representative samples is a main focus of my research, and in this talk I'll touch on two specific applications from statistical physics and combinatorics. Another main contribution of my research has been applying these same Markov chain processes used for sampling in a novel way to address research questions in programmable matter and swarm robotics, where a main goal is to understand how simple computational elements can accomplish complicated system-level goals. In a constrained setting, we've answered this question by showing groups of abstract particles executing our simple processes, derived from Markov chains, can provably accomplish remarkable global objectives.

Kravis Center 102, CMC Campus

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