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Gerard Ben Arous

Professor of Mathematics

    1982 …2019
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    Research Output 1982 2019

    Article

    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

    Aging in the random energy model

    Arous, G. B., Bovier, A. & Gayrard, V., Feb 25 2002, In : Physical Review Letters. 88, 8

    Research output: Contribution to journalArticle

    energy
    spin glass
    traps

    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

    Aging of spherical spin glasses

    Arous, G. B., Dembo, A. & Guionnet, A., May 2001, In : Probability Theory and Related Fields. 120, 1, p. 1-67 67 p.

    Research output: Contribution to journalArticle

    Spin Glass
    Invariant Measure
    Phase Transition
    Langevin Dynamics
    Equilibrium Measure

    Annulation plate du noyau de la chaleur hypoelliptique

    Ben Arous, G. & Léandre, R., 1991, In : Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 312, p. 463-464

    Research output: Contribution to journalArticle

    A probabilistic approach to semi-classical approximations

    Ben Arous, G. & Castell, F., Apr 10 1996, In : Journal of Functional Analysis. 137, 1, p. 243-280 38 p.

    Research output: Contribution to journalArticle

    Semiclassical Approximation
    Probabilistic Approach
    Wave Function
    Wiener Measure
    Caustic

    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

    Asymptotic survival probabilities in the random saturation process

    Arous, G. B. & Ramírez, A. F., Oct 2000, In : Annals of Probability. 28, 4, p. 1470-1527 58 p.

    Research output: Contribution to journalArticle

    Survival Probability
    Saturation
    Injection
    Trap
    Asymptotic Behavior

    Asymptotiques presque sûres des probabilités de survie dans le processus de saturation aléatoire

    Translated title of the contribution: Quenched asymptotics for survival probabilities in the random saturation processBen Arous, G. & Ramírez, A. F., Dec 1 1999, In : Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 329, 11, p. 1003-1008 6 p.

    Research output: Contribution to journalArticle

    Survival Probability
    Saturation
    Trap
    Random Environment
    Enlargement

    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

    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

    Biased random walks on random graphs

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

    Research output: Contribution to journalArticle

    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

    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

    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

    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

    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

    Decroissance exponentielle du noyau de la chaleur sur la diagonale (I)

    Ben Arous, G. & Léandre, R., Jun 1991, In : Probability Theory and Related Fields. 90, 2, p. 175-202 28 p.

    Research output: Contribution to journalArticle

    Décroissance exponentielle du noyau de la chaleur sur la diagonale (II)

    Arous, G. B. & Léandre, R., Sep 1991, In : Probability Theory and Related Fields. 90, 3, p. 377-402 26 p.

    Research output: Contribution to journalArticle

    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

    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

    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

    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

    Flots et series de Taylor stochastiques

    Arous, G. B., Feb 1989, In : Probability Theory and Related Fields. 81, 1, p. 29-77 49 p.

    Research output: Contribution to journalArticle

    Flow decomposition and large deviations

    Arous, G. B. & Castell, F., Aug 25 1996, In : Journal of Functional Analysis. 140, 1, p. 23-67 45 p.

    Research output: Contribution to journalArticle

    Large Deviations
    Decompose
    Nonlinear Filtering
    Decomposition Theorem
    Diffusion Process

    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

    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

    Géométrie de la courbe brownienne plane

    Ben Arous, G., 1992, In : Asterisque. 201-202-203

    Research output: Contribution to journalArticle

    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

    Holder norms and the support theorem for diffusions

    Ben Arous, G., Ledoux, M. & Gradinaru, M., 1994, In : Annales de l'Institut Henri Poincaré. 30, 3, p. 415-436

    Research output: Contribution to journalArticle

    Increasing propagation of chaos for mean field models

    Arous, G. B. & Zeitouni, O., Jan 1999, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 35, 1, p. 85-102 18 p.

    Research output: Contribution to journalArticle

    Propagation of Chaos
    Mean-field Model
    Asymptotic Independence
    Langevin Dynamics
    Relative Entropy

    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

    Laplace asymptotics for reaction-diffusion equations

    Arous, G. B. & Rouault, A., Mar 1993, In : Probability Theory and Related Fields. 97, 1-2, p. 259-285 27 p.

    Research output: Contribution to journalArticle

    Reaction-diffusion Equations
    Laplace
    Small Parameter
    Logarithmic

    Large deviations and the Strassen theorem in Hölder norm

    Baldi, P., Ben Arous, G. & Kerkyacharian, G., 1992, In : Stochastic Processes and their Applications. 42, 1, p. 171-180 10 p.

    Research output: Contribution to journalArticle

    Brownian movement
    Large Deviations
    Logarithm laws
    Topology
    Norm

    Large deviations for Brownian motion on the Sierpinski gasket

    Arous, G. B. & Kumagai, T., Feb 1 2000, In : Stochastic Processes and their Applications. 85, 2, p. 225-235 11 p.

    Research output: Contribution to journalArticle

    Sierpinski Gasket
    Large Deviation Principle
    Rate Function
    Brownian movement
    Large Deviations

    Large deviations for Langevin spin glass dynamics

    Arous, G. B. & Guionnet, A., Dec 1995, In : Probability Theory and Related Fields. 102, 4, p. 455-509 55 p.

    Research output: Contribution to journalArticle

    Spin Glass
    Large Deviations
    Empirical Measures
    Large Deviation Principle
    Path Space

    Large deviations for Langevin spin glass dynamics

    Arous, G. B. & Guionnet, A., Sep 1995, In : Probability Theory and Related Fields. 103, 3, p. 431 1 p.

    Research output: Contribution to journalArticle

    Large deviations

    Large deviations for Wigner's law and Voiculescu's non-commutative entropy

    Ben Arous, G. & Guionnet, A., Aug 1997, In : Probability Theory and Related Fields. 108, 4, p. 517-542 26 p.

    Research output: Contribution to journalArticle

    Spectral Measure
    Large Deviations
    Large Deviation Principle
    Entropy
    Rate Function

    Large deviations from the circular law

    Ben Arous, G. & Zeitouni, O., 1998, In : ESAIM: Probability and Statistics. 2, p. 123-134

    Research output: Contribution to journalArticle

    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

    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

    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

    Metastability for dynamics of the 3D Ising model

    Ben Arous, G. & Cerf, R., 1996, In : Electronic Journal in Probability. 1

    Research output: Contribution to journalArticle

    Metastability
    Ising Model
    Torus
    Magnetic Field
    Three-dimensional