Faculty Research Perspectives
Geometric Functional Inequalities and the Kac Model
Eric CarlenMarch 10, 3:30 PM in Hill 705
Abstract.
Mathematical Physics continues to be wonderful source of interesting problems in pure mathematics. This will be illustrated in this lecture by introducing some problems that I have worked on, and others that I am working on, that derive from one such model -- The Kac Model.
The Kac model is a model of a gas of N molecules undergoing binary collisions that conserve energy and momentum in terms of a certain simple and natural random walk on a high dimensional (for large N) sphere. There are a number of mathematically and physically interesting questions about the rate at which this random walk forgets its starting point, so that the distribution of its location on the sphere tends to the uniform distribution.