About me
I'm a PhD candidate working with Prof Krzysztof Burdzy in the probability theory group at the University of Washington, Seattle, and am also in the statistics department getting a concurrent masters.
My research interests are in stochastic processes, particularly interacting diffusions. Two projects which I am currently working: Using discrete approximations to calculate invariant measures for interacting diffusions; categorizing reflection laws for random billiards whose velocity and spatial components have an invariant measure of product form.The image adjacent to the photo (of myself in Valparaiso) was generated by a group of undergraduates I worked with in the Washington eXperimental Math Lab (WXML). They used computational methods to confirm conjectures for the Hausdorff dimension of the Brownian earthworm model. See their report. They compared two computational methods to estimate the Hausdorff dimension of fractals. Check out this list of fractals and their Hausdorff dimension.
Contact: clayton.barnes[at]math.washington.edu