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Gerard Ben Arous

Professor of Mathematics

    1982 …2019
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    Research Output 1982 2019

    2015

    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

    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
    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