Seminar on Free Probability
and Random Matrices

Fall 2015

Organizer: J. Mingo

  Schedule for Current Term

Thursday, December 3, 4:30 - 6:00, Jeff 110
Jamie Mingo (Queen's)
Second Order Cumulants of Partially Transposed Matrices, II
This will be a continuation from November 26.

Thursday, November 26, 4:30 - 6:00, Jeff 110
Jamie Mingo (Queen's)
Second Order Cumulants of Partially Transposed Matrices
I will review the construction of second order cumulants and work out the semi-circular case. I will then show how to compute these for partially transposed Wishart matrices.
Thursday, November 19, 4:30 - 6:00, Jeff 110
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness: a free probability study of fluctuations of random matrices, III
This will be a continuation from November 5.
Thursday, November 5, 4:30 - 6:00, Jeff 110
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness: a free probability study of fluctuations of random matrices, II
This will be a continuation from the previous week.
Thursday, October 29, 4:30 - 6:00, Jeff 110
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness: a free probability study of fluctuations of random matrices
Second order freeness is a feature exhibited in the large $N$ limit by random matrix ensembles such as the orthogonal Gaussian random matrices and the orthogonal Wishart random matrices. Its main purpose is to help determine the asymptotic behaviour of the covariance of traces of products of random matrices; this is comparable to the description of the asymptotic behaviour of the expectation of the trace of products of random matrices that we get from freeness. In this talk, we will give the definition of second order freeness and present some of the most relevant work related to it
Thursday, October 8, 4:30 - 6:00, Jeff 110
Mario Diaz (Queen's)
On the Speed at which Asymptotic Liberation Sequences Deliver Freeness
It is well known that certain ensembles of unitary matrices deliver asymptotic freeness under suitable conditions. Related to the intuitive question about how random an ensemble must be in order to deliver freeness, Anderson and Farrell found a unitary ensemble which is “less random” than the Haar distributed ensemble originally proposed by Voiculescu. In this talk we propose to study the speed at which these ensembles deliver freeness as an alternative measure of “randomness”. This is joint work with Jamie Mingo.
Thursday, October 1, 4:30 - 6:00, Jeff 110 (note room change)
Jamie Mingo (Queen's)
The Partial Transpose of Unitary and Orthogonal Matrices, II
This will be a continuation from last week.
Tuesday, September 22, 4:30 - 6:00, Jeff 422
Jamie Mingo (Queen's)
The Partial Transpose of Unitary and Orthogonal Matrices
In quantum information theory a frequently used test for entanglement is the positive partial transpose test. For a Wishart matrix Aubrun found the aspect ratio that guarantees a non-positive positive partial transpose and thus entanglement. Mihai Popa and I considered the interaction between a Widget matrix and its partial transpose. We showed that the matrix, its full transpose and its partial transposes are asymptotically free. In this talk I will consider what happens when we consider orthogonal and unitary matrices.
Tuesday, September 15, 4:30 - 6:00, Jeff 422
Emily Redelmeier
Matrix Cumulants and the Topological Expansion
I will discuss how matrix cumulants, defined by Capitaine and Casalis (2007) in terms of a convolution, connect to diagrammatic methods of calculating matrix integrals, and how these tools are particularly useful in the multi-matrix setting. I will focus on the real case, and consider also how the complex case is related. I will also discuss how this approach is useful in the quaternionic case, in particular in problems involving partial traces.

I will also discuss some of the tools useful for analyzing the non-orientable diagrams which appear in the real and quaternionic cases.

Previous Schedules

Fall 2010 Fall 2011 Fall 2012 Fall 2013 Fall 2014
Winter 2011 Winter 2012 Winter 2013 Winter 2014 Winter 2015
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

Getting to Jeffery Hall from the Hotel Belvedere