Mini-Workshop of the ANR STARS

Contribution List

13. Lunch

6/26/23, 12:30 PM

1. Talk by Camille Male

Camille Male

6/26/23, 2:00 PM

9. Talk by Issa Dabo

Issa Dabo

6/26/23, 3:30 PM

4. Large deviations for the top eigenvalue of deformed random matrices

Benjamin McKenna

6/27/23, 9:45 AM

In recent years, the few classical results in large deviations for random matrices have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with Harish-Chandra/Itzykson/Zuber integrals. We present one such result, focusing on extreme eigenvalues of deformed sample-covariance and Wigner random matrices. This confirms recent...

5. Talk by Stéphane Dartois

Stéphane Dartois

6/27/23, 11:15 AM

14. Lunch

6/27/23, 12:30 PM

6. Martingale Theoretic Approach to Noncommutative Stochastic Calculus

Vaki Nikitopoulos

6/28/23, 9:30 AM

Free -- or more generally noncommutative -- stochastic analysis is often useful for describing the large $N$-limit of an ensemble $X^{(N)} = \big(X_t^{(N)}\big)_{t \geq 0}$ of $N \times N$ matrix stochastic processes. We describe a flexible general theory of noncommutative stochastic calculus that is useful for describing the large-$N$ limits of solutions to $N \times N$ matrix stochastic...

7. Injective norm of random tensors

Ion Nechita

6/28/23, 11:00 AM

I will present some new results about the injective norm of random tensors. The distributions we shall consider range from the simplest Gaussian distribution to that of symmetric Gaussian tensors or random Matrix Product States, which are of interest in quantum information theory. This is joint work in progress with Cécilia Lancien

15. Lunch

6/28/23, 12:30 PM

8. Dinner

6/28/23, 8:00 PM

2. Pitman's theorem and the quantum group SL2 in infinite curvature

François Chapon

6/29/23, 9:30 AM

Pitman's theorem states that a Brownian motion minus twice its current minimum is a Markov process. We will consider two a priori distinct approaches to this theorem: Biane's approach, using a non-commutative walk on the quantum group SL2 in the crystal regime "q=0", and Bougerol-Jeulin's approach, using Brownian motion on the hyperbolic space with infinite curvature. A unified version of...

11. Small cycle structure for words in conjugacy invariant random permutations

Slim Kammoun

6/29/23, 11:00 AM

We are interested in the cycle structure of words in several random permutations.
The first part of the talk will be dedicated to recall classic results (Nica 1994) when the permutations are i.i.d uniform of size n.

In the second part, we assume that the permutations are independent and that their distribution is conjugacy invariant, with a good control on their short cycles. If, after...

17. Lunch

6/29/23, 12:30 PM

10. How to estimate a covariance matrix? Hopefully in large dimensions.

Reda Chhaibi

6/30/23, 9:30 AM

Consider the basic operation of estimating the spectrum of large covariance matrices.
This estimation has an inherent "large dimensional bias", when one observes a multivariate sample whose size is comparable to the dimension.
Solving this issue amounts to understanding free multiplicative deconvolution.
Our work follows the footsteps of El Karoui, Arizmendi-Tarrago-Vargas and...

12. Between free groups and surface groups.

6/30/23, 11:00 AM

We shall consider free groups of arbitrary finite, even rank, and their quotient by one relator leading to surface groups. The aim of the talk is to present different families of traces on the free group, that interpolate between the regular trace on the quotient and the regular trace on the free group, while being motivated by matrix approximations. When the rank is 2, the non-commutative...

16. Lunch

6/30/23, 12:30 PM

3. Colloquium : Some aspects of Horn's problem

Jean-Bernard Zuber

6/30/23, 2:00 PM

Horn's problem deals with the following question: what can be said about the spectrum
of eigenvalues of the sum 𝐶=𝐴+𝐵 of two Hermitian matrices of given spectrum ? The support of the spectrum of 𝐶 is now well understood, after a long series of works from Weyl (1912) to Horn (1952) to Klyachko (1998) and Knutson and Tao (1999). The problem has also amazing connections with group theory and...