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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