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Ivan Corwin (IICD member and professor of mathematics) and Eric Corwin (University of Oregon, Physics) were recently awarded a $1,000,000 W.M. Keck foundation Science and Engineering grant to study "Extreme Diffusion". Over one hundred years ago Einstein created a remarkably simple and powerful theory describing the behavior of a single diffusing particle. That theory has since been applied countless times to successfully model widely disparate systems. However, when a large number of particles are diffusing in the same environment, that theory neglects the effect of the shared environment in which all particles coexist. The Corwin brothers plan to demonstrate (theoretically, numerically and experimentally) that due to this neglect, Einstein's theory dramatically fails to predict the behavior of extreme diffusion, i.e., the outlier particles which have moved the farthest from their starting points. By synthesizing their experimental measures and theoretical results, they will define a new "extreme diffusion coefficient" which succinctly describes these extreme behaviors and provides a window into the internal correlation structure of the environment in which diffusion occurs. Understanding the behavior of outliers will have wide ranging applicability to physical, biological, epidemiological, economic, and social systems where outliers often determine behavior.
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