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Large Deviations in Random Matrix Theory

Project information

Grant agreement ID: 884584

Status

Grant agreement signed

  • Start date

    1 September 2020

  • End date

    31 August 2025

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 2 384 537,50

  • EU contribution

    € 2 384 537,50

Hosted by:

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

France

Objective

Large deviations theory develops the art of estimating the probability of rare events. The classical theory concentrates on the study of the probability of deviating from the behavior predicted by the law of large numbers, namely the probability that the empirical mean of independent variables differs from its expectation. Such a classical framework does not apply in random matrix theory where one deals with complicated functions of independent variables or strongly interacting random variables, for instance the eigenvalues of a matrix with independent entries. During the last twenty years, important advances allowed to analyze large deviations for a few specific models of random matrices, but a full understanding of these questions is still missing. The object of this project is to develop such a theory. Two notable examples motivate this project. The first is to understand how the distribution of the entries of a random matrix affects the probability of the rare events of its spectrum as its dimension goes to infinity. The second is to prove in great generality the convergence of matrix integrals and Voiculescu's microstates entropy, as well as analyze their limit. The impact of this project would go beyond probability and operator algebra as it would apply to other fields such as theoretical physics, statistics and statistical learning.
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Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

Address

Rue Michel Ange 3
75794 Paris

France

Activity type

Research Organisations

EU Contribution

€ 2 384 537,50

Beneficiaries (1)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

France

EU Contribution

€ 2 384 537,50

Project information

Grant agreement ID: 884584

Status

Grant agreement signed

  • Start date

    1 September 2020

  • End date

    31 August 2025

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 2 384 537,50

  • EU contribution

    € 2 384 537,50

Hosted by:

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

France