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Guillaume Cébron10/06/2024 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.
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François Chapon10/06/2024 14:00
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Guillaume Cébron10/06/2024 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.
Aller à la page de la contribution -
François Chapon11/06/2024 10:00
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Guillaume Cébron11/06/2024 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.
Aller à la page de la contribution -
François Chapon11/06/2024 16:30
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Guillaume Cébron12/06/2024 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.
Aller à la page de la contribution -
Capitaine Mireille13/06/2024 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...
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François Chapon13/06/2024 14:00
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Capitaine Mireille13/06/2024 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...
Aller à la page de la contribution -
Chhaibi Reda14/06/2024 09:30
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Capitaine Mireille14/06/2024 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...
Aller à la page de la contribution -
Chhaibi Reda14/06/2024 14:00
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Chhaibi Reda14/06/2024 16:00
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Alice Guionnet17/06/2024 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.
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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.... -
Gérard Ben Arous17/06/2024 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.
Aller à la page de la contribution
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized... -
Jamal Najim17/06/2024 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,...
Aller à la page de la contribution -
Alice Guionnet17/06/2024 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.
Aller à la page de la contribution
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.... -
Gérard Ben Arous18/06/2024 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.
Aller à la page de la contribution
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized... -
Alice Guionnet18/06/2024 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.
Aller à la page de la contribution
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.... -
Jamal Najim18/06/2024 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,...
Aller à la page de la contribution -
Gérard Ben Arous18/06/2024 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.
Aller à la page de la contribution
I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized...
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