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Texas A&M University
Mathematics

Probability Seminar

Date: January 29, 2018

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: paul jung, Korea Advanced Institute of Science and Technology

  

Title: Infinite-volume Gibbs measures for the 1D-Coulomb jellium

Abstract: 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 (non-ergodicity of the Gibbs measures) at low densities of electrons. Using tools from probability theory including the Feyman-Kac formula and Markov chains, we demonstrate crystallization for the quantum one-dimensional jellium at all densities.