Student Probability
Organizer: Jiyun Park
Upcoming Events
Past Events
I will continue our discussion of techniques for proving superconcentration paricularly in energy models. Specifically, we'll cover why Talagrand's inequality is useful for monotone functions but not some others, and we'll analyze the Ornstein-Uhlenbeck process in more detail to provide an…
I will cover the method of establishing superconcentration via hypercontractive inequalities with two examples: Talagrand's Gaussian L1-L2 inequality and the KKL inequality for Boolean functions. The basic definitions and identities involving semigroups and the dirichlet form will be covered for…
I will introduce the book "Superconcentration and Related Topics" by Sourav Chatterjee, which will be the topic of this quarter's seminar. Superconcentration occurs when classical concentration of measure gives suboptimal bounds on the order of fluctuations. I will go over several examples…
Abstract
One of the main topics of study in first-passage percolation is the time constant, whose level sets can be thought of as the limit shape. Interestingly, the convergence of the scaled first passage time to the time-constant can be viewed as a stochastic homogenization problem for a…