##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Jay Cummings

#### UCSD

## Edge flipping in the complete graph

##### Abstract:

Given a graph, perform the following randomized coloring procedure to it: pick an edge at random and with probability $p$ color the end vertices of that edge blue; otherwise color them red. Repeat indefinitely, choosing the edges with replacement. This induces a random walk in the space of all red/blue colorings of the graph, which converges to a stationary distribution. In this talk we will study this stationary distribution for the complete graph with the goal of getting Jay a PhD.

Advisor: Ron Graham

### May 19, 2016

### 1:00 PM

### AP&M 6402

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