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Gerard Ben Arous

Professor of Mathematics

    1982 …2019
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    Research Output 1982 2019

    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

    Stable Limit Laws for Reaction-Diffusion in Random Environment

    Ben Arous, G., Molchanov, S. & Ramírez, A. F., Jan 1 2019, Probability and Analysis in Interacting Physical Systems - In Honor of S.R.S. Varadhan, 2016. Olla, S., Friz, P., König, W. & Mukherjee, C. (eds.). Springer New York LLC, p. 123-171 49 p. (Springer Proceedings in Mathematics and Statistics; vol. 283).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Limit Laws
    Random Environment
    Reaction-diffusion
    Fluctuations
    Rank One Perturbation

    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

    Comparing Dynamics: Deep Neural Networks versus Glassy Systems

    Baity-Jest, M., Sagun, L., Mario, G., Spiglery, S., Ben Arous, G., Cammarota, C., LeCun, Y., Vvyart, M. & Biroli, G. J., Jan 1 2018, 35th International Conference on Machine Learning, ICML 2018. Krause, A. & Dy, J. (eds.). International Machine Learning Society (IMLS), Vol. 1. p. 526-535 10 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Physics
    Deep neural networks

    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

    Explorations on high dimensional landscapes

    Sagun, L., Ugur Güney, V., Ben Arous, G. & LeCun, Y., Jan 1 2015.

    Research output: Contribution to conferencePaper

    Spin glass
    student teacher
    Students
    simulation
    experiment

    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

    Second order expansion for implied volatility in two factor local stochastic volatility models and applications to the dynamic λ-Sabr model

    Ben Arous, G. & Laurence, P., 2015, Large Deviations and Asymptotic Methods in Finance. Springer New York LLC, Vol. 110. p. 89-136 48 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Implied Volatility
    Stochastic Volatility Model
    Dynamic Model
    Volatility
    Financial Mathematics

    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

    The Loss Surfaces of Multilayer Networks

    Choromanska, A., Henaff, M. B., Mathieu, M., Ben Arous, G. & LeCun, Y., 2015, International Conference on Articial Intelligence and Statistics (AISTATS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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 energy landscapes

    Ben Arous, G., Jan 1 2013, XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012. World Scientific Publishing Co., p. 403 1 p.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    replicas
    broken symmetry
    critical point
    topology
    energy

    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

    Wigner matrices

    Ben Arous, G. & Guionnet, A., 2010, Handbook on random matrices. Ackemann, G., Baik, J. & Di Francesco, P. (eds.). Oxford University Press, p. 433-451 Chapter 21

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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

    REM universality for random hamiltonians

    Ben Arous, G. & Kuptsov, A., 2009, Progress in Probability. Basel, Switzerland: Birkhauser, Vol. 62. p. 45-84 39 p.

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    2008

    A new REM conjecture

    Ben Arous, G., Gayrard, V. & Kuptsov, A., 2008, In and out of equilibrium. Sidoravicius, V. & Vares, M. (eds.). Birkhauser Verlag, Basel, Switzerland: Birkhauser, p. 59-96 37 p. (Progress in Probability; vol. 60).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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

    Stochastic analysis in mathematical physics

    Ben Arous, G. (ed.), Cruzeiro, A. B. (ed.), Jan, Y. L. (ed.) & Zambrini, J-C. (ed.), 2007, Proceedings of a Satellite Conference of ICM 2006. Lisbon, Portugal. September 4-8, 2006. World Scientific

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    Transition asymptotics for reaction-diffusion in random media

    Ben Arous, G., Ramírez, A. F. & Molchanov, S., 2007, Probability and mathematical physics: A volume in honor of Stanislav Molchanov. Providence, RI: American Mathematical Society, p. 1-40 (CRM Proc. Lecture Notes; vol. 42).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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