S4F5 - Graduate Seminar on Interacting Random Systems

 

Time, room	Thursday 14-16, LWK 0.011
Supervision	Patrik Ferrari (LWK 3.047) and Pedro Cardoso (LWK 3.048)
Contact	If you have any questions, in particular if you would like to sign up for the seminar, please contact me via email (see my homepage).

 

Subject: Interacting particles and random matrices

In the lecture of stochastic analysis, we have mention towards the end that for some given initial conditions, the large time limit of the solution of the KPZ equation converges to a distribution called GUE Tracy-Widom distribution. I also told to the students who were in the lecture that this distribution has first been discovered in the framework of random matrices, as describing the limit distribution of the largest eigenvalue of a large hermitian matrix.

In this seminar we are going to focus on the question
Why random matrices share universal processes with interacting particle systems?

More precisely, we will consider on one side a system of interacting particles in 2+1 dimensions and on the other side some random matrix models. We will see that the connection between the two, a-priori unrelated worlds, can be explained by considering the mathematical structure in the background.

One of the references for the seminar will be this one.

For the 2+1 dimensional model, you can look at this animation.

The exact list of topics will be made once I have a rough idea of the number of students participating to the graduate seminar. If you are interested in the seminar, but you were not in my lecture on July 9th where I presented the topic, you can contact me also via email (that you find in my homepage). To sign up to the seminar or to get further information, write me an email.