### Hitting Times for Generalized Ehrenfest Urn Models

##### Project Abstract

The original two-urn Ehrenfest model can be represented by a random walk on a graph for describing the diffusion of gas molecules between two isolated bodies. For a random walk on a graph, the hitting time from node A to node B is the minimum number of steps the random walk takes to reach node B for the first time when the random walk initially starts at node A. The expected hitting times associated with the two-urn model are well studied, but little work is known for the multiple-urn model. This project is to investigate how to compute numerous expected hitting times under the generalized multiple-urn Ehrenfest models. In particular, we will explore the electric network approach in our investigation.