Summer school EUR MINT 2024 "Random Matrices and Free Probability"

Liste des contributions

8. Introduction to free probability 1/4

Guillaume Cébron

10/06/2024 09:00

The aim of this course is to present the concept of free independence, the related central limit theorem, the notion of free cumulants, and the use of free independence to study large random matrices.

9. Introduction to random matrices 1/4

François Chapon

10/06/2024 14:00

10. Introduction to free probability 2/4

Guillaume Cébron

10/06/2024 16:30

The aim of this course is to present the concept of free independence, the related central limit theorem, the notion of free cumulants, and the use of free independence to study large random matrices.

6. Introduction to random matrices 2/4

François Chapon

11/06/2024 10:00

11. Introduction to free probability 3/4

Guillaume Cébron

11/06/2024 14:00

The aim of this course is to present the concept of free independence, the related central limit theorem, the notion of free cumulants, and the use of free independence to study large random matrices.

13. Introduction to random matrices 3/4

François Chapon

11/06/2024 16:30

12. Introduction to free probability 4/4

Guillaume Cébron

12/06/2024 10:00

The aim of this course is to present the concept of free independence, the related central limit theorem, the notion of free cumulants, and the use of free independence to study large random matrices.

5. Deformed matricial models and free probability theory 1/3

Capitaine Mireille

13/06/2024 10:00

Practical problems naturally lead to wonder about the spectrum reaction of a given random matrix after a deterministic perturbation. For example, in the signal theory, the deterministic perturbation is seen as the signal, the perturbed matrix is perceived as a "noise" and the question is to know whether the observation of the spectral properties of "signal plus noise" can give access to...

14. Introduction to random matrices 4/4

François Chapon

13/06/2024 14:00

15. Deformed matricial models and free probability theory 2/3

Capitaine Mireille

13/06/2024 16:30

Practical problems naturally lead to wonder about the spectrum reaction of a given random matrix after a deterministic perturbation. For example, in the signal theory, the deterministic perturbation is seen as the signal, the perturbed matrix is perceived as a "noise" and the question is to know whether the observation of the spectral properties of "signal plus noise" can give access to...

4. Beta ensembles 1/3

Chhaibi Reda

14/06/2024 09:30

16. Deformed matricial models and free probability theory 3/3

Capitaine Mireille

14/06/2024 11:30

Practical problems naturally lead to wonder about the spectrum reaction of a given random matrix after a deterministic perturbation. For example, in the signal theory, the deterministic perturbation is seen as the signal, the perturbed matrix is perceived as a "noise" and the question is to know whether the observation of the spectral properties of "signal plus noise" can give access to...

17. Beta ensembles 2/3

Chhaibi Reda

14/06/2024 14:00

18. Beta ensembles 3/3

Chhaibi Reda

14/06/2024 16:00

3. Large deviations for the largest eigenvalues of random matrices 1/3

Alice Guionnet

17/06/2024 09:00

Estimating the probabilities of large deviations of extreme eigenvalues of random matrices is necessary to estimate the volume of minima of random functions.
In general, this is a difficult question, as the law of these
eigenvalues is not explicit. In this course, we will
discuss the known results in this field, and the different methods of obtaining them, as well as open problems....

1. Random matrices and dynamics of optimization in very high dimensions 1/3

Gérard Ben Arous

17/06/2024 11:00

Machine learning and Data science algorithms include the need for efficient optimization of topologically complex random functions in very high dimensions. Surprisingly, simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively.
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized...

2. Equilibria in large Lotka-Volterra systems of ODE coupled by large random matrices 1/2

Jamal Najim

17/06/2024 14:00

Large Lotka-Volterra (LV) systems of coupled ODE are a popular model for complex systems in interaction, in particular large ecological systems. Since the « real » coupling between the differential equations is in general out of reach, a coupling based on the realization of a large random matrix is often used in practice. Within this framework, we shall discuss the existence of an equilibrium,...

19. Large deviations for the largest eigenvalues of random matrices 2/3

Alice Guionnet

17/06/2024 16:45

Estimating the probabilities of large deviations of extreme eigenvalues of random matrices is necessary to estimate the volume of minima of random functions.
In general, this is a difficult question, as the law of these
eigenvalues is not explicit. In this course, we will
discuss the known results in this field, and the different methods of obtaining them, as well as open problems....

22. Random matrices and dynamics of optimization in very high dimensions 2/3

Gérard Ben Arous

18/06/2024 09:00

Machine learning and Data science algorithms include the need for efficient optimization of topologically complex random functions in very high dimensions. Surprisingly, simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively.
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized...

21. Large deviations for the largest eigenvalues of random matrices 3/3

Alice Guionnet

18/06/2024 11:00

Estimating the probabilities of large deviations of extreme eigenvalues of random matrices is necessary to estimate the volume of minima of random functions.
In general, this is a difficult question, as the law of these
eigenvalues is not explicit. In this course, we will
discuss the known results in this field, and the different methods of obtaining them, as well as open problems....

20. Equilibria in large Lotka-Volterra systems of ODE coupled by large random matrices 2/2

Jamal Najim

18/06/2024 14:00

Large Lotka-Volterra (LV) systems of coupled ODE are a popular model for complex systems in interaction, in particular large ecological systems. Since the « real » coupling between the differential equations is in general out of reach, a coupling based on the realization of a large random matrix is often used in practice. Within this framework, we shall discuss the existence of an equilibrium,...

23. Random matrices and dynamics of optimization in very high dimensions 3/3

Gérard Ben Arous

18/06/2024 16:45

Machine learning and Data science algorithms include the need for efficient optimization of topologically complex random functions in very high dimensions. Surprisingly, simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively.
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized...