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Gerard Ben Arous

Professor of Mathematics

    1982 …2019
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    Research Output 1982 2019

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    2019

    Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions

    Ros, V., Ben Arous, G., Biroli, G. & Cammarota, C., Jan 4 2019, In : Physical Review X. 9, 1, 011003.

    Research output: Contribution to journalArticle

    Open Access
    ruggedness
    tensors
    energy
    glass
    rice

    Scaling limit for the ant in a simple high-dimensional labyrinth

    Ben Arous, G., Cabezas, M. & Fribergh, A., Jun 1 2019, In : Probability Theory and Related Fields. 174, 1-2, p. 553-646 94 p.

    Research output: Contribution to journalArticle

    Brownian Excursion
    Branching Random Walk
    Simple Random Walk
    Scaling Limit
    Rescaling

    Scaling Limit for the Ant in High-Dimensional Labyrinths

    Ben Arous, G., Cabezas, M. & Fribergh, A., Apr 1 2019, In : Communications on Pure and Applied Mathematics. 72, 4, p. 669-763 95 p.

    Research output: Contribution to journalArticle

    Brownian movement
    Scaling Limit
    Critical Graph
    High-dimensional
    Higher Dimensions

    The Landscape of the Spiked Tensor Model

    Ben Arous, G., Mei, S., Montanari, A. & Nica, M., Jan 1 2019, (Accepted/In press) In : Communications on Pure and Applied Mathematics.

    Research output: Contribution to journalArticle

    Tensors
    Tensor
    Polynomials
    Maximum likelihood
    Critical point
    2018

    Spectral Gap Estimates in Mean Field Spin Glasses

    Ben Arous, G. & Jagannath, A., May 19 2018, (Accepted/In press) In : Communications in Mathematical Physics. p. 1-52 52 p.

    Research output: Contribution to journalArticle

    Spectral Gap
    Spin Glass
    Mean Field
    spin glass
    Free Energy
    2015

    A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases

    Ben Arous, G., Fribergh, A. & Sidoravicius, V., 2015, (Accepted/In press) In : Communications on Pure and Applied Mathematics. To appear.

    Research output: Contribution to journalArticle

    On fluctuations of eigenvalues of random permutation matrices

    Arous, G. B. & Dang, K., May 1 2015, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 51, 2, p. 620-647 28 p.

    Research output: Contribution to journalArticle

    Permutation Matrix
    Random Permutation
    Random Matrices
    Fluctuations
    Statistics
    Loss Function
    Multilayer
    Open Problems
    Multilayers
    Spin glass

    Randomly trapped random walks

    Ben Arous, G., Cabezas, M., Černý, J. & Royfman, R., 2015, In : arXiv. 1302.7227.

    Research output: Contribution to journalArticle

    The loss surfaces of multilayer networks

    Choromanska, A., Henaff, M., Mathieu, M., Ben Arous, G. & LeCun, Y., 2015, In : Journal of Machine Learning Research. 38, p. 192-204 13 p.

    Research output: Contribution to journalArticle

    Multilayer
    Multilayers
    Hamiltonians
    Spin glass
    Feedforward neural networks
    2014

    Biased random walks on random graphs

    Arous, G. B. & Fribergh, A., Jun 19 2014, In : arXiv.

    Research output: Contribution to journalArticle

    Explorations on high dimensional landscapes

    Sagun, L., Guney, V. U., Arous, G. B. & LeCun, Y., Dec 20 2014, In : arXiv.

    Research output: Contribution to journalArticle

    Lyons-Pemantle-Peres Monotonicity Problem for High Biases

    Ben Arous, G., Fribergh, A. & Sidoravicius, V., Apr 2014, In : Communications on Pure and Applied Mathematics. 67, 4, p. 519-530 12 p.

    Research output: Contribution to journalArticle

    Galton-Watson Tree
    Biased
    Monotonicity
    Random walk
    Leaves

    Smallest Singular Value for Perturbations of Random Permutation Matrices

    Arous, G. B. & Dang, K., Apr 15 2014, In : arXiv.

    Research output: Contribution to journalArticle

    The Loss Surfaces of Multilayer Networks

    Choromanska, A., Henaff, M., Mathieu, M., Arous, G. B. & LeCun, Y., Nov 30 2014, In : arXiv.

    Research output: Contribution to journalArticle

    2013

    A Central Limit Theorem in Many-Body Quantum Dynamics

    Ben Arous, G., Kirkpatrick, K. & Schlein, B., Jul 2013, In : Communications in Mathematical Physics. 321, 2, p. 371-417 47 p.

    Research output: Contribution to journalArticle

    Quantum Dynamics
    Central limit theorem
    theorems
    Hartree Equation
    Mean-field Limit

    Complexity of random smooth functions on the high-dimensional sphere

    Auffinger, A. & Arous, G. B., Nov 2013, In : Annals of Probability. 41, 6, p. 4214-4247 34 p.

    Research output: Contribution to journalArticle

    Random Function
    Smooth function
    High-dimensional
    Critical value
    Gaussian Function

    Einstein relation for biased random walk on Galton-Watson trees

    Arous, G. B., Hu, Y., Olla, S. & Zeitouni, O., Aug 2013, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 49, 3, p. 698-721 24 p.

    Research output: Contribution to journalArticle

    Galton-Watson Tree
    Albert Einstein
    Biased
    Random walk
    Random Media

    Extreme gaps between eigenvalues of random matrices

    Arous, G. B. & Bourgade, P., 2013, In : Annals of Probability. 41, 4, p. 2648-2681 34 p.

    Research output: Contribution to journalArticle

    Random Matrices
    Extremes
    Limiting
    Eigenvalue
    Unitary matrix

    Random matrices and complexity of spin glasses

    Auffinger, A., Arous, G. B. & Černý, J., Feb 2013, In : Communications on Pure and Applied Mathematics. 66, 2, p. 165-201 37 p.

    Research output: Contribution to journalArticle

    Spin glass
    Spin Glass
    Random Matrices
    Hamiltonians
    Energy Landscape
    2012

    Biased random walks on Galton-Watson trees with leaves

    Ben Arous, G., Fribergh, A., Gantert, N. & Hammond, A., Jan 2012, In : Annals of Probability. 40, 1, p. 280-338 59 p.

    Research output: Contribution to journalArticle

    Galton-Watson Tree
    Increment
    Biased
    Random walk
    Leaves

    Preface: From the Director

    Arous, G. B., Jul 2012, In : Communications on Pure and Applied Mathematics. 65, 7, p. 889-890 2 p.

    Research output: Contribution to journalArticle

    Randomly biased walks on subcritical trees

    Ben Arous, G. & Hammond, A., Nov 2012, In : Communications on Pure and Applied Mathematics. 65, 11, p. 1481-1527 47 p.

    Research output: Contribution to journalArticle

    Walk
    Biased
    Decomposition
    Conductance
    Decay

    Universality and extremal aging for dynamics of spin glasses on subexponential time scales

    Ben Arous, G. & Gün, O., Jan 2012, In : Communications on Pure and Applied Mathematics. 65, 1, p. 77-127 51 p.

    Research output: Contribution to journalArticle

    Spin glass
    Spin Glass
    Universality
    Time Scales
    Aging of materials
    2011

    Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture

    Ben Arous, G. & Corwin, I., Jan 2011, In : Annals of Probability. 39, 1, p. 104-138 35 p.

    Research output: Contribution to journalArticle

    Current Fluctuations
    Passage Time
    Scaling Function
    Fluctuations
    Fluctuation Theorem
    2010

    Free point processes and free extreme values

    Arous, G. B. & Kargin, V., Feb 2010, In : Probability Theory and Related Fields. 147, 1, p. 161-183 23 p.

    Research output: Contribution to journalArticle

    Extreme Values
    Point Process
    Poisson Random Measure
    Limit Laws
    Order Statistics
    2009

    Poisson convergence for the largest eigenvalues of heavy tailed random matrices

    Auffinger, A., Ben Arous, G. & Péchéb, S., Aug 2009, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 45, 3, p. 589-610 22 p.

    Research output: Contribution to journalArticle

    Sample Covariance Matrix
    Largest Eigenvalue
    Random Matrices
    Siméon Denis Poisson
    Asymptotic Behavior
    2008

    Elementary potential theory on the hypercube

    Arous, G. B. & Gayrard, V., Oct 4 2008, In : Electronic Journal of Probability. 13, p. 1726-1807 82 p., 59.

    Research output: Contribution to journalArticle

    Hitting Time
    Potential Theory
    Hypercube
    Harmonic Measure
    Diverge

    The arcsine law as a universal aging scheme for trap models

    Ben Arous, G. & Černý, J., Mar 2008, In : Communications on Pure and Applied Mathematics. 61, 3, p. 289-329 41 p.

    Research output: Contribution to journalArticle

    Arc-sine Law
    Trap
    Aging of materials
    Subordinator
    Energy Model

    The spectrum of heavy tailed random matrices

    Arous, G. B. & Guionnet, A., Mar 2008, In : Communications in Mathematical Physics. 278, 3, p. 715-751 37 p.

    Research output: Contribution to journalArticle

    Random Matrices
    Eigenvalue
    Converge
    entry
    Stable Laws

    Universality of random energy model-like ageing in mean field spin glasses

    Arous, G. B., Bovier, A. & Černý, J., Apr 1 2008, In : Journal of Statistical Mechanics: Theory and Experiment. 2008, 4, L04003.

    Research output: Contribution to journalArticle

    Energy Model
    Spin Glass
    Mean Field
    spin glass
    Universality

    Universality of the REM for dynamics of mean-field spin glasses

    Ben Arous, G., Bovier, A. & Černý, J., Sep 2008, In : Communications in Mathematical Physics. 282, 3, p. 663-695 33 p.

    Research output: Contribution to journalArticle

    Spin Glass
    Mean Field
    spin glass
    Universality
    Subordinator
    2007

    Scaling limit for trap models on ℤd

    Arous, G. B. & Černý, J., 2007, In : Annals of Probability. 35, 6, p. 2356-2384 29 p.

    Research output: Contribution to journalArticle

    Scaling Limit
    Trap
    Subordinator
    Time Change
    Brownian motion
    2006

    Aging in two-dimensional Bouchaud's model

    Arous, G. B., Černý, J. & Mountford, T., Jan 2006, In : Probability Theory and Related Fields. 134, 1, p. 1-43 43 p.

    Research output: Contribution to journalArticle

    Correlation Function
    Markov chain
    Random variable
    Model

    Course 8 Dynamics of trap models

    Arous, G. B. & Černý, J., 2006, In : Les Houches Summer School Proceedings. 83, C, p. 331-394 64 p.

    Research output: Contribution to journalArticle

    traps

    Cugliandolo-Kurchan equations for dynamics of spin-glasses

    Ben Arous, G., Dembo, A. & Guionnet, A., Dec 2006, In : Probability Theory and Related Fields. 136, 4, p. 619-660 42 p.

    Research output: Contribution to journalArticle

    Langevin Dynamics
    Nonlinear Integro-differential Equations
    Mean-field Model
    Statistical Physics
    Spin Glass

    Free extreme values

    Ben Arous, G. & Voiculescu, D. V., Sep 2006, In : Annals of Probability. 34, 5, p. 2037-2059 23 p.

    Research output: Contribution to journalArticle

    Extreme Values
    Peaks over Threshold
    Free Probability
    Extreme Value Theory
    Poisson Point Process
    2005

    Bouchaud's model exhibits two aging regimes in dimension 1

    Ben Arous, G. & Černý, J., 2005, In : Annals of applied probability. 15, 2, p. 1161-1192

    Research output: Contribution to journalArticle

    Limit theorems for sums of random exponentials

    Ben Arous, G., Bogachev, L. V. & Molchanov, S. A., Jul 2005, In : Probability Theory and Related Fields. 132, 4, p. 579-612 34 p.

    Research output: Contribution to journalArticle

    Limit Theorems
    Regular Variation
    Characteristic Exponents
    H-function
    Limit Laws

    Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices

    Baik, J., Arous, G. B. & Péché, S., Sep 2005, In : Annals of Probability. 33, 5, p. 1643-1697 55 p.

    Research output: Contribution to journalArticle

    Sample Covariance Matrix
    Largest Eigenvalue
    Limiting Distribution
    Covariance matrix
    Phase Transition

    Transition from the annealed to the quenched asymptotics for a random walk on random obstacles

    Ben Arous, G., Molchanov, S. & Ramírez, A. F., Nov 2005, In : Annals of Probability. 33, 6, p. 2149-2187 39 p.

    Research output: Contribution to journalArticle

    Survival Probability
    Random walk
    Infinitely Divisible Laws
    Characteristic Exponents
    Decrease

    Universality of local eigenvalue statistics for some sample covariance matrices

    Arous, G. B. & Péché, S., Oct 2005, In : Communications on Pure and Applied Mathematics. 58, 10, p. 1316-1357 42 p.

    Research output: Contribution to journalArticle

    Sample Covariance Matrix
    Gaussian distribution
    Covariance matrix
    Probability distributions
    Universality
    2004

    Spatio-temporal large deviations principle for coupled circle maps

    Bardet, J. B. & Arous, G. B., Jan 2004, In : Annals of Probability. 32, 1 B, p. 692-729 38 p.

    Research output: Contribution to journalArticle

    Circle Map
    Coupled Maps
    Large Deviation Principle
    Dynamical system
    Thermodynamic Formalism
    2003

    A two armed bandit type problem

    Benaïm, M. & Arous, G. B., Dec 2003, In : International Journal of Game Theory. 32, 1, p. 3-16 14 p.

    Research output: Contribution to journalArticle

    Multi-armed Bandit
    Multi-armed bandit

    Glauber dynamics of the random energy model: II. Aging below the critical temperature

    Ben Arous, G., Bovier, A. & Gayrard, V., May 2003, In : Communications in Mathematical Physics. 236, 1, p. 1-54 54 p.

    Research output: Contribution to journalArticle

    Long-time Asymptotics
    Glauber Dynamics
    Energy Model
    Long-time Behavior
    Autocorrelation Function

    Glauber dynamics of the random energy model I. Metastable motion on the extreme states

    Ben Arous, G., Bovier, A. & Gayrard, V., Apr 2003, In : Communications in Mathematical Physics. 235, 3, p. 379-425 47 p.

    Research output: Contribution to journalArticle

    Glauber Dynamics
    Energy Model
    Jump
    Extremes
    Time of Arrival

    Internal DLA in a random environment

    Ben Arous, G., Quastel, J. & Ramírez, A. F., Mar 2003, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 39, 2, p. 301-324 24 p.

    Research output: Contribution to journalArticle

    Random Environment
    Trap
    Internal
    Random walk
    Euclidean

    Large deviations in the Langevin dynamics of a random field Ising model

    Arous, G. B. & Sortais, M., Jun 1 2003, In : Stochastic Processes and their Applications. 105, 2, p. 211-255 45 p.

    Research output: Contribution to journalArticle

    Langevin Dynamics
    Ising model
    Empirical Process
    Large Deviations
    Random Field

    Large deviations in the Langevin dynamics of a short-range spin glass

    Ben Arous, G. & Sortais, M., Dec 2003, In : Bernoulli. 9, 6, p. 921-954 34 p.

    Research output: Contribution to journalArticle

    Langevin Dynamics
    Empirical Process
    Spin Glass
    Large Deviations
    Interacting Diffusions

    Multiscale Homogenization with Bounded Ratios and Anomalous Slow Diffusion

    Arous, G. B. & Owhadi, H., Jan 2003, In : Communications on Pure and Applied Mathematics. 56, 1, p. 80-113 34 p.

    Research output: Contribution to journalArticle

    Brownian movement
    Homogenization
    Anomalous
    Periodic Potential
    Superposition