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Mathematical Sciences

The Ehrenfest Urn Model

Date: 3:30pm - 4:30pm PDT November 2, 2017 Location: John Howard 115

John Howard 115

The Ehrenfest Urn Model

by William DeLee and Lars Mayrand

The two-urn Ehrenfest model is a classical Markov chain that can be used to describe many natural processes such as gas diffusion. If a and b are two states of a Markov chain, the hitting time from state a to state b is the number of steps that the chain takes to reach state for the first time when the chain initially starts at state a. While hitting time problems associated with the two-urn model are well-studied, we focus on a variety of hitting times under a generalized Ehrenfest urn model with two or more urns. In particular, we use the electric network approach to obtain simple closed-form expressions for the expected hitting times for filling and emptying urns.