2020 - Member of the National Academy of Sciences
2015 - Fellow of the American Academy of Arts and Sciences
Gérard Ben Arous mostly deals with Random matrix, Statistical physics, Eigenvalues and eigenvectors, Mathematical analysis and Combinatorics. As a part of the same scientific study, Gérard Ben Arous usually deals with the Random matrix, concentrating on Probability distribution and frequently concerns with Equidistributed sequence, Absolute continuity, Lebesgue measure, Empirical distribution function and Almost surely. His research integrates issues of Random energy model, Spin glass, Energy, Glauber and Gaussian in his study of Statistical physics.
His work in Eigenvalues and eigenvectors tackles topics such as Matrix which are related to areas like Tracy–Widom distribution. The various areas that Gérard Ben Arous examines in his Mathematical analysis study include Riemann curvature tensor, Large deviations theory and Pure mathematics. His Combinatorics research is multidisciplinary, incorporating perspectives in Covariance matrix, Estimation of covariance matrices, Statistics and Complex normal distribution.
Statistical physics, Combinatorics, Random walk, Spin glass and Mathematical analysis are his primary areas of study. The study incorporates disciplines such as Dynamics, Maxima and minima, Random energy model, Observable and Gaussian in addition to Statistical physics. Gérard Ben Arous has researched Combinatorics in several fields, including Lambda and Random matrix, Eigenvalues and eigenvectors.
His Random matrix research incorporates themes from Absolute continuity, Pure mathematics, Lebesgue measure, Equidistributed sequence and Probability measure. His Eigenvalues and eigenvectors research integrates issues from Complex normal distribution, Covariance matrix and Matrix. His studies in Mathematical analysis integrate themes in fields like Thermal diffusivity, Large deviations theory and Brownian motion.
Gérard Ben Arous spends much of his time researching Statistical physics, Spin glass, Langevin dynamics, Gibbs measure and Applied mathematics. His Statistical physics research is multidisciplinary, incorporating elements of Brownian motion, Random graph, Random walk, Scaling and Lie algebra. His work in Spin glass addresses issues such as Mixing, which are connected to fields such as Eigenvalues and eigenvectors, Mean field theory, Spectral gap, Phase boundary and Phase.
The concepts of his Gibbs measure study are interwoven with issues in Hamiltonian and Distribution. His Applied mathematics course of study focuses on Exponential function and Gaussian, High dimensional and Linear estimation. The Polynomial study combines topics in areas such as Random matrix and Pure mathematics.
Gérard Ben Arous focuses on Tensor, Gaussian, Gibbs measure, Distribution and Spin glass. His Tensor research includes themes of Phase transition, Polynomial, Expected value and Unit sphere. His work investigates the relationship between Gaussian and topics such as Principle of maximum entropy that intersect with problems in Langevin dynamics and Pointwise.
The various areas that Gérard Ben Arous examines in his Gibbs measure study include Hamiltonian and Radius. The concepts of his Distribution study are interwoven with issues in Eigenvalues and eigenvectors, Spectral gap, Mean field theory, Point and Mixing. His work on Spin glass is being expanded to include thematically relevant topics such as Statistical physics.
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The Loss Surface of Multilayer Networks.
Anna Choromanska;Mikael Henaff;Michaël Mathieu;Gérard Ben Arous.
The Loss Surfaces of Multilayer Networks
Anna Choromanska;Mikael Henaff;Michael Mathieu;Gérard Ben Arous.
international conference on artificial intelligence and statistics (2015)
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik;Gérard Ben Arous;Sandrine Péché;Sandrine Péché.
Annals of Probability (2005)
Random matrices and complexity of spin glasses
Antonio Auffinger;Gérard Ben Arous;Jiří Černý.
Communications on Pure and Applied Mathematics (2013)
Universality of local eigenvalue statistics for some sample covariance matrices
Gérard Ben Arous;Sandrine Péché.
Communications on Pure and Applied Mathematics (2005)
Flots et series de Taylor stochastiques
Gérard Ben Arous.
Probability Theory and Related Fields (1989)
Complexity of random smooth functions on the high-dimensional sphere
Antonio Auffinger;Gerard Ben Arous.
Annals of Probability (2013)
The Spectrum of Heavy Tailed Random Matrices
Gérard Ben Arous;Gérard Ben Arous;Alice Guionnet.
Communications in Mathematical Physics (2008)
Glauber Dynamics of the Random Energy Model . I. Metastable Motion on the Extreme States
Gérard Ben Arous;Anton Bovier;Véronique Gayrard.
Communications in Mathematical Physics (2003)
Methods de laplace et de la phase stationnaire sur l'espace de wiener
Gérard Ben Arous.
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