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Colloquium, Spring 2005

Day: Tuesday May 17th Time: 4:00pm Place: BH 112 Title: Hermit Crabs: The Benefits of Vacancies Speaker: Amber Hixson, WWU Abstract: Imagine you are a little hermit crab, Hermie, living at the bottom of a tide pool. You are growing in your little shell and you want to move up in the world by acquiring a bigger shell. Lucky you! A space has opened up in the shell next door. You hurry out of your small shell into a nice roomy shell that is just right. In the meantime, Squirmy, a smaller hermit crab decides to take over your vacant shell. Bernie takes over Squirmy's shell and so on. Thus we can see that the original vacant shell benefited more than one crab. In my talk, we will discover Finite Markov Chains through the example of a random walk. I will show you how we can use Finite Markov chains to model Hermie and his friends' path to acquisition of a shell that is just right. Finite Markov Chains combine probability and linear algebra to model such processes. We will calculate to what extent the introduction of a certain size of shell can help other hermit crabs of different sizes, and which vacancy benefits the largest number of crabs. If time permits, I will also discuss other models using Markov Chains. Cookies: In BH 300 at 3:30pm.