Probability Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/29 2:00pm 
BLOC 628 
paul jung Korea Advanced Institute of Science and Technology 
Infinitevolume Gibbs measures for the 1DCoulomb jellium
The jellium is a model, introduced by Wigner, for a gas of electrons moving in a uniform neutralizing background of positive charge. In two dimensions, the model is related to the Gaussian free field while in one dimension the model is used to study dimerization and crystallization. For the quantum 1D jellium, Brascamp and Lieb (1975) proved crystallization (nonergodicity of the Gibbs measures) at low densities of electrons. Using tools from probability theory including the FeymanKac formula and Markov chains, we demonstrate crystallization for the quantum onedimensional jellium at all densities. 

02/26 2:00pm 
BLOC 220 
Erik Lundberg Florida Atlantic University 
Random matrices arising in the study of random fields
Certain problems in random fields, such as studying the solutions to a random system of equations (e.g., the critical points of a random potential energy landscape) have made important use of random matrix theory. After surveying some applications related to classical random matrix ensembles, we present a new direction in random fields concerning the solutions to problems in enumerative geometry (e.g., the number of lines on a random cubic surface). The resulting random matrices are of a special structured type. We conclude with some open problems that are simple to state. This is joint work with Saugata Basu, Antonio Lerario, and Chris Peterson. 
Archives
Please direct inquiries to
Eviatar Procaccia.