Seminar on Free Probability
and Random Matrices

Fall 2022

Organizers: Jamie Mingo and Troy Day

  Schedule for Current Term

Upcoming talks       Previous Schedules




Tuesday, November 8 , 11:00 - 12:00, Jeff 202
Jamie Mingo (Queen's)
Introduction to Wishart Matrices and the Marchenko-Pastur law, IV
I will conclude this week by using Stieltjes inversion to find the density of the Marchenko-Pastur Law. Notes
Tuesday, November 1 , 11:00 - 12:00, Jeff 202
Jamie Mingo (Queen's)
Introduction to Wishart Matrices and the Marchenko-Pastur law, III
This week I will continue the discussion of the relation between the moment and free-cumulant generating functions. We then will see what this means for the Marchenko-Pastur Law. Notes
Tuesday, October 25 , 11:00 - 12:00, Jeff 202
Jamie Mingo (Queen's)
Introduction to Wishart Matrices and the Marchenko-Pastur law, II
This week I will present the relation between the moment and free-cumulant generating functions. We then will see what this means for the Marchenko-Pastur Law. Notes
Tuesday, October 18 , 11:00 - 12:00, Jeff 202
Jamie Mingo (Queen's)
Introduction to Wishart Matrices and the Marchenko-Pastur law
I will review the construction of a Wishart matrix and the moments of it eigenvalue distribution. In the following weeks I will show how to find the distribution of the large N limit and interpret it in terms of non-crossing partitions. I will keep the exposition elementary and accessible. Notes

Tuesday, October 4, 11:00 - 12:00, Jeff 202
Pedro Rangel (Queen's)
Moments of complex Gaussian random vectors
Contining the discussion from last week, we will discuss Gaussian random vectors and their moments.


Tuesday, September 27, 11:00 - 12:00, Jeff 202
Daniel Muñoz (Queen's)
Moments and cumulants of random variables, Part II
In our previous meeting we talked about the moments and the cumulants associated to a random variable. We introduced the cumulants from two approaches, in one hand an analytic approach, while in the other hand a more combinatorial one. For this talk, we will prove these two definitions are equivalents. We will talk in further detail about the combinatorial definition and see how the moment-cumulant relation can be achieved via the mobius inversion theorem. We will see how it is possible to extend the cumulants to multilinear functions and recast a multilinear version of the moment-cumulant relation. If time permits, we will introduce some matrix models of interest in Random Matrix Theory.

Tuesday, September 20, 11:00 - 12:00, Jeff 202
Daniel Muñoz (Queen's)
Moments and cumulants of random variables, Part I
Given a random variable with all its moments, it is possible to expand the logarithm of its characteristic function as a power series. The coefficients on this series are called the cumulants of the random variable. Cumulants turns out to be a quite interesting object as they describe properties that the moments may not. I will introduce the concept of cumulants, or “classical cumulants”, from two different perspectives, in one hand a complete analytic definition while in the other hand a more combinatorial definition, as we will check, those two definitions are equivalent. We will compute these cumulants for popular cases such as the Gaussian case. Most of the talk will be based in section 1.1 “Moments and cumulants of random variables” from “Free probability and random matrices” by Mingo and Speicher, while some other results may be based on “Lectures on the combinatorics of free probability” by Nica and Speicher.

Upcoming Talks





Previous Schedules

Fall 2017 Fall 2018 Fall 2019 Fall 2021
Winter 2018 Winter 2019 Winter 2020 Winter 2021 Winter 2022
Fall 2010 Fall 2011 Fall 2012 Fall 2013 Fall 2014 Fall 2015 Fall 2016
Winter 2011 Winter 2012 Winter 2013 Winter 2014 Winter 2015 Winter 2016 Winter 2017
Fall 2003 Fall 2004 Fall 2005 Fall 2006 Fall 2007 Fall 2008 Fall 2009
Winter 2004 Winter 2005 Winter 2006 Winter 2007 Winter 2008 Winter 2009 Winter 2010