# Seminar on Free Probability and Random Matrices Fall 2017

## Organizer: J. Mingo <!-- // // format date as dd-mmm-yy // example: 12-Jan-99 // function date_ddmmmyy(date) { var d = date.getDate(); var m = date.getMonth() + 1; var y = date.getYear(); // handle different year values // returned by IE and NS in // the year 2000. if(y >= 2000) { y -= 2000; } if(y >= 100) { y -= 100; } // could use splitString() here // but the following method is // more compatible var mmm = ( 1==m)?'Jan':( 2==m)?'Feb':(3==m)?'Mar': ( 4==m)?'Apr':( 5==m)?'May':(6==m)?'Jun': ( 7==m)?'Jul':( 8==m)?'Aug':(9==m)?'Sep': (10==m)?'Oct':(11==m)?'Nov':'Dec'; return "" + (d<10?"0"+d:d) + "-" + mmm + "-" + (y<10?"0"+y:y); } // // get last modified date of the // current document. // function date_lastmodified() { var lmd = document.lastModified; var s = "Unknown"; var d1; // check if we have a valid date // before proceeding if(0 != (d1=Date.parse(lmd))) { s = "" + date_ddmmmyy(new Date(d1)); } return s; } // // finally display the last modified date // as DD-MMM-YY // document.write( "Last modified on " + date_lastmodified() ); // -->   Schedule for Current Term

Thursday, November 30, 4:00 - 5:30, Jeff 319
Pei-Lun Tseng (Queen's University)
Infinitesimal Laws of non-commutative random variables, II
In this talk, we will focus on a single type B variable, and introduce the corresponding infinitesimal law. In addition, we will also define the free additive convolution for infinitesimal laws, and to see the relation between the type B laws and the infinitesimal laws.

Thursday, November 23, 4:00 - 5:30, Jeff 319
Pei-Lun Tseng (Queen's University)
Infinitesimal Laws of non-commutative random variables
In this talk, we will start from an infinitesimal non-commutative probability space, and define the freeness, and additive convolution for infinitesimal laws. Then, we will also establish the relation among type A free convolution, type B free convolution, and infinitesimal free convolution.

Tuesday, November 14, 3:30 - 5:00, Jeff 222
Pei-Lun Tseng (Queen's University)
Free independence of type B
We will continue our discussion of type B R-transform. Then we are going to introduce the free independence of type B, and establish the relation between type B freeness and vanishing mixed cumulants in type B.

Tuesday, November 7, 3:30 - 5:00, Jeff 319
Pei-Lun Tseng (Queen's University)
Non-crossing cumulants of type B
In this talk, we are going to introduce the framework of type B non-commutative probability space. Then, we will give the definition of the cumulants of type B and show the relation between the cumulants of type A and the cumulants of type B.  Finally, we will discuss the corresponding moments series and R-transform of type B.

Tuesday, October 31, 4:00 - 5:30, Jeff 319
Caleb Jonker (Queen's University)
Traffic Free Probability Spaces and Operad Independence
The discussion of non-commutative independence revolves around what are known as universal products on non-commutative probability spaces. These were defined by Roland Speicher in a paper showing that there are only three such products, yielding free independence, tensor (classical) independence and Boolean independence. We will expand Speicher's definition of independence to more general types of probability spaces focusing much of our discussion around the notion of traffic free independence.

Thursday, October 19, 4:00 - 5:30, Jeff 319
Josué Daniel Vázquez Becerra (Queen's University)
Liberation and the bounded cumulants property, part II
In this talk, we will show that conjugation by certain random unitary liberating matrices delivers the bounded cumulants property.

Tuesday, October 10, 4:00 - 5:30, Jeff 319
Caleb Jonker (Queen's University)
Traffic Free Probability Spaces and Operad Independence
The discussion of non-commutative independence revolves around what are known as universal products on non-commutative probability spaces. These were defined by Roland Speicher in a paper showing that there are only three such products, yielding free independence, tensor (classical) independence and Boolean independence. We will expand Speicher's definition of independence to more general types of probability spaces focusing much of our discussion around the notion of traffic free independence.

Tuesday, October 10, 4:00 - 5:30, Jeff 319
Josué Daniel Vázquez Becerra (Queen's University)
Liberation and the bounded cumulants property
In this talk, we will show that conjugation by certain random unitary liberating matrices delivers the bounded cumulants property.

Tuesday, October 3, 1:30 - 2:30, Jeff 319
Jamie Mingo (Queen's University)
The Role of the Transpose in Free Probability:
the partial transpose of R-cyclic operators, Part III
I will continue from last week.

Monday, September 25, 1:30 - 2:30, Jeff 319
Jamie Mingo (Queen's University)
The Role of the Transpose in Free Probability:
the partial transpose of R-cyclic operators, Part II
I will continue from last week.

Tuesday, September 19, 4:00 - 5:30, Jeff 319
Jamie Mingo (Queen's University)
The Role of the Transpose in Free Probability:
the partial transpose of R-cyclic operators
Like tensor independence, free independence gives us rules for doing calculations. With random matrix models, we usually need tensor independence of the entries and some kind of group invariance of the joint distribution of the entries to get the (asymptotic) freeness necessary to apply the tools of free probability.

A few years ago Mihai Popa and I found that the transpose also produces asymptotic freeness, i.e. a matrix could be asymptotically free from its own transpose. Since that we have expanded this work to the case of the partial transposes that arise in quantum information theory.

In this talk I will explain what happens when one transposes certain R-cyclic operators.

Previous Schedules

Getting to Jeffery Hall from the Hotel Belvedere