# Random Matrix & Probability Theory Seminar

In the In the 2019-2020 AY, the Random Matrix and Probability Theory Seminar will take place on Thursdays from 3:15 – 4:15pm in CMSA, room G02. The list below will reflect the dates of the scheduled talks. The list will be updated as the details are confirmed.

The schedule will be updated as details are confirmed.

 Date Speaker Title/Abstract 9/11/2019 Subhabrata Sen Title: Sampling convergence for random graphs: graphexes and multigraphexes Abstract: We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch ’17). Sam- pling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara. 9/25/2019 Jeff Schenker (Michigan State) Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states  Abstract: Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one — “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh) 10/11/2019   Friday 3:30pm Room G10 Michael Aizenman, Princeton TBA 10/16/2019 10/23/2019 10/30/2019 11/6/2019 11/13/2019 11/20/2019 11/27/2019 12/4/2019 12/11/2019

For information on previous seminars, click here