Photo of Gérard Ben Arous Gérard BEN AROUS

Courant Institute of Mathematical Sciences
New York University

Professor of Mathematics
Director of the Courant Institute
Vice Provost for Science and Engineering Development

251 Mercer Street
New York, NY 10012
benarous[at]cims[dot]nyu[dot]edu

For assistance, please reach out to:

Lena Jane Carey
Office of the Director
CIMS
lenajanecarey[at]nyu[dot]edu






Biography

Department of Mathematics
Courant Institute
New York University
Publications

91. Randomly Trapped Random Walks, with Manuel Cabezas, Jiří Černý and Roman Royfman, submitted arXiv:1302.7227

90.  A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases, with Alexander Fribergh and Vladas Sidoravicius, to appear in Communications in Pure and Applied Mathematics

89.  On Fluctuations of Eigenvalues of Random Permutation matrices, with Kim Dang, to appear in Annales de l’Institut Henri Poincaré, arXiv 1106.2108

88.  Complexity of random Smooth functions of many variables, with Anotonio Auffinger, to appear in Annals of Probability, arXiv 1110.5872

87.  A Central Limit theorem in many body Quantum dynamics, with Kay Kirkpatrick and Benjamin Schlein, Communications in Mathematical Physics, Vol. 321, No. 2, pp 371-417,2013

     
86. Random Matrices and Complexity of Spin Glasses, with Antonio Auffinger and Jiří Černý, Communications in Pure and Applied Mathematics, Vol. 66, No. 2, 165-201, 2013

85.  Einstein relation for biased random walks on Galton-Watson trees, with Yueyun Hu, Stefano Olla and Ofer Zeitouni, Annales de l’Institut Henri Poincaré, Vol. 49, No. 3, 698-721, 2013

84.  Extreme gaps between eigenvalues of random matrices, with Paul Bourgade, Annals of Probability, Vol. 41, No. 4, 2648-2681, 2013

83.  Universality and extremal aging for dynamics of Spin Glasses on subexponential time scales, with Onur Gün, Communications in Pure and Applied Mathematics, Vol. LXV, No1, pp 77-127, 2012

82.   Randomly biased walks on subcritical trees, with Alan Hammond, Communications in Pure and Applied Mathematics, Vol. 65, No. 11, 1481-1527, 2012
                 
81.   Biased random walks on Galton-Watson trees with leaves, with Alexander Fribergh, Nina Gantert, Alan Hammond, Annals of Probability, Vol. 40, No. 1, 280-338, 2012

80.   Current Fluctuations for TASEP, a proof of the Praehofer Spohn conjecture, with Ivan Corwin, Annals of Probability, Vol. 39, no. 1, 104-138, 2011

79.   Wigner Matrices, with Alice Guionnet, pp 433-451, Chapter 21 in “Handbook on Random Matrices”, edited by G. Ackemann, Jinho Baik, Philippe Di Francesco, Oxford University Press, 2010 

78.    Free point-processes and free extreme values, with Vladislav Kargin, Probability Theory and Related Fields, Vol. 147, No 1-2, pp 161-183, 2010

77.    Poisson convergence for the largest eigenvalues of heavy-tailed random matrices, with Anotonio Auffinger and Sandrine Péché, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 45, No. 3, pp 589–610, 2009

76.    REM Universality for Random Hamiltonians, with Alexey Kuptsov, Progress in Probability, Vol. 62, pp 45–84,Birkhauser Verlag, Basel, Switzerland, 2009

75.    Universality of the REM for dynamics of mean-field spin glasses, with Anton Bovier and Jiří Černý, Communications in Mathematical Physics, Vol. 282, pp. 633—695, 2008

74.    Heavy Tailed Wigner Matrices, with Alice Guionnet, Communications in Mathematical Physics, Vol. 278, Number 3, pp 715-751, 2008

73 . Universality of Random Energy Model like aging in mean field spin glasses, with Anton Bovier and Jiří Černý, 
Journal of Statistical Mechanics: Theory and Experiment, No. 4, L04003, 2008

72.  A new REM conjecture, With Veronique Gayrard and Alexey Kuptsov, In and Out of Equilibrium, editors Vladas Sidoravicius and Maria Eulalia Vares, Progress in Probability, Birkhauser, Volume 60, pp 59-96, 2008

71.  Elementary Potential theory on the hypercube, with Veronique Gayrard, Electronic Journal of Probability, Volume 13, pp 1726-1807, 2008

70.  The Arcsine Law as a universal aging scheme for Trap models, with Jiří Černý, Communications in Pure and Applied Mathematics, vol 61, No 3, pp 289-329, 2008

69.  STOCHASTIC ANALYSIS IN MATHEMATICAL PHYSICS, Proceedings of a Satellite Conference of ICM 2006 Lisbon, Portugal 4 - 8 September 2006, edited with Ana Bela Cruzeiro, Yves Le Jan & Jean-Claude Zambrini, World Scientific, 2007

68.  Scaling limits for trap models on Z^d, with Jiří Černý, The Annals of Probability. Volume 35, Number 6, pp 2356-2384, 2007

67.  Transition asymptotics for reaction-diffusion in random media, with Alejandro Ramirez and Stanislav Molchanov, Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, 1-40, CRM Proc. Lecture Notes,  vol 42, Amer. Math. Soc., Providence, RI, 2007

66.   Dynamics of Trap Models, with Jiří Černý, in Mathematical Statistical Physics Lecture Notes, Vol LXXXIII Les Houches Summer School, Elsevier, 2006

65.   Cugliandolo-Kurchan Equations for dynamics of Spin Glasses, with Amir Dembo and Alice Guionnet, Probability Theory and Related Fields, vol 136, n°4, pp 619-660, 2006

64.   Extreme Values In Free Probability, with Dan Voiculescu, Annals of Probability, vol 34, n°5, pp 2037-2059, 2006

63.   Aging for Bouchaud’s trap model in dimension 2, with Jiří Černý and Thomas Mountford, Probability Theory and Related Fields, vol 134, n°1, pp 1-43, 2006

62.   Phase transition for the largest eigenvalue of large sample covariance matrices, with Jinho Baik and Sandrine Péché, Annals of Probability vol 33, n° 5, pp 1643-1697, 2005

61.   Universality of local eigenvalue statistics for sample covariance matrices, with Sandrine Péché, Communications of Pure and Applied Mathematics, vol 58, n°10, pp 1316-1357, 2005

60.   Bouchaud's model exhibits two aging regimes in dimension 1, with, Jiří Černý, Annals of Applied Probability vol 15, n°2, pp 1161-1192, 2005

59.   Limit Laws for Sums of Random Exponentials, with Leonid Bogatchev and Stanislav Molchanov, Probability Theory and Related Fields, vol 132, n°4, pp 579-612, 2005

58.   Transition from the annealed to the quenched asymptotics for random walkson random obstacles, with Stanislav Molchanov and Alejandro Ramirez, Annals of Probability, vol 33, n° 6, pp 2149-2187, 2005

57.    Limit Laws for Sums of Random Exponentials, with Leonid Bogatchev and Stanislav Molchanov, Recent developments in Stochastic Analysis and related topics, pp 45-65, World Scientific, Hackensack, NJ, 2004

56.    Algorithms for Stochastic Approximations of Curvature Flows, with Gozde Unal, Delphine Nain, Nahum Shimkin, Allen Tannenbaum and Ofer Zeitouni, Proceedings of ICIP, 2004

55.    Spatio-temporal large deviations principle for coupled circle maps, with Jean-Baptiste Bardet, Annals of  Probability, vol 32 n°1, pp 692-729, 2004

54.    Large Deviations in the Langevin dynamics of a short range spin glass, with Michel Sortais, Bernoulli, vol 9 n°6, pp 921-954, 2003

53.    A two armed-bandit type problem, with Michel Benaim, International Journal of Game Theory, vol 32, pp 3-16, 2003

52.    Multiscale homogenization with bounded ratios and anomalous slow diffusion, with Houman Owhadi, Communications in Pure and Applied mathematics, vol 56 n°1, pp 80-113, 2003
 
51.    Internal DLA in a random environment, with Jeremy Quastel and Alejandro Ramirez, Annales de l’Institut Henri Poincaré, vol 39 n°2, pp 301-324, 2003

50.    Glauber dynamics of the random energy model. II. Aging below the critical temperature, with Anton Bovier and Veronique Gayrard, Communications in Mathematical Physics, vol 236 n°1, pp1-54, 2003 

49.     Glauber dynamics of the random energy model. I. Metastable motion on the extreme states, with Anton Bovier and Veronique Gayrard, Communications in Mathematical Physics, vol 235 n°3, pp 379-425, 2003

48.     Large deviations in the Langevin dynamics of a random field Ising model, with Michel Sortais, Stochastic Processes and Applications, vol 105 n°2, pp 211-255, 2003

47.     Crystalline Stochastic Systems and curvature driven flows, with Allen Tannenbaum and Ofer Zeitouni, pp 41-63, Mathematical Systems theory in Biology, Communications and Finance, IMA volume in Mathematics and its Applications 134, Springer, New York  Editors J.Rosenthal and D. Gilliam, 2003

46.      Stochastic approximations to curve-shortening flows via particle systems, with Allen Tannenbaum and Ofer Zeitouni. Journal of Differential Equations, vol 195 n°1, pp 119-142, 2003

45.       Aging and spin-glass dynamics. Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), pp 3-14, Higher Ed. Press, Beijing, 2002

44.       Phase transition for the spherical hierarchical model, with Ostap Hryniv and Stanislav Molchanov, Markov Processes and Related Fields, vol 8 n°4, pp 565-594, 2002
 
43.       Aging in the Random Energy Model, with Anton Bovier and Veronique Gayrard, Vol 8, issue 88, Phys.Rev Letters, 2002

42.       Super-diffusivity in a shear flow model from perpetual homogenization, with Houman Owhadi, Communications in Mathematical Physics, vol 227 n°2, pp 281-302, 2002
 
41.       The canonical equation of adaptive dynamics: a mathematical view, with Nicolas Champagnat and Denise R. Ferriere, Selection, vol 2, pp 71-81, 2001

40.       Aging of spherical spin glasses, with Amir Dembo and Alice Guionnet, Probability Theory and Related Fields, Vol 120 no 1, pp 1-67, 2001
 
39.       Growth and saturation in random media, with Alejandro Ramirez. Stochastic processes, physics and geometry: new interplays, 41--54, CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000

38.       Asymptotic survival probabilities in the random saturation process, with Alejandro Ramirez, The Annals of Probability, Vol 28, no. 4, pp 1470—1527, 2000

37.       Large deviations of Brownian motion on the Sierpinski gasket, with Takashi Kumagai, Stochastic Process and Applications, Vol 85 no. 2, pp 225—235, 2000

36.       Quenched asymptotics for survival probabilities in the random saturation process, with Alejandro Ramirez, C.R. Acad. Sci. Paris, p. 1003-1008, 1999

35.       Increasing propagation of chaos for mean field models, with Ofer Zeitouni, Annales de l'IHP, vol 35, pp85-102, 1999

34.       Large deviations from the circular law, with Ofer Zeitouni, ESAIM: Probability and Statistics, Vol. 2, pp. 123-134, 1998

33.       Singularity of hypoelliptic Green functions, with Mihai Gradinaru. Potential Analysis and Applications, vol 8,pp 217-258, 1998

32.       Langevin Dynamics for Sherrington-Kirkpatrick Spin Glasses, avec Alice Guionnet, chapter of the book: " Mathematical Aspects of Spin Glasses and Neural Networks ", pp. 321-
353, Progress in Probability, No 41,  Birkhauser, 1998

31.       Symmetric Langevin Spin Glass Dynamics, with Alice Guionnet, Annals of Probability, vol. 25, No 3, pp1367-1422, 1997

30.       Large deviations for Wigner's law and Voiculescu's non commutative entropy, with Alice Guionnet, Probability theory and related fields, volume 108, 4, pp 517-542,1997

29.       Singularités des fonctions de Green hypoelliptiques, with Mihai Gradinaru, Annales Mathématiques, Blaise Pascal, vol 3, 1996

28.       Metastability for dynamics of the 3D Ising model, with Raphaël Cerf, Electronic Journal in Probability, vol 1, 1996

27.       The Construction of the d-dimensional Gaussian Droplet, with J-D Deuschel, Communications in Math, Physics, vol 179, pp 467-488, 1996

26.       A probabilistic approach to semi-classical approximations, with Faber Castell, Journal of Functional Analysis, vol 137, pp 243-280, 1996

25.       Flow Decomposition and Large Deviations, with Faber Castell, Journal of Functional Analysis, vol 140, pp 23-67, 1996

24.       Large deviations for Langevin Spin Glass Dynamics, Erratum, with Alice Guionnet, Probability theory and related fields, 102, pp 455-509, 1995

23.       Coupling constructions for hypoelliptic diffusions, with Michael Cranston and Wilfred Kendall, Proceedings of Symposia in Pure mathematics, AMS, 1994, pp 193-213, 1994

22.       Grandes déviations de Freidlin-Wentzell en norme holderienne, with Michel Ledoux. Séminaire de Probabilités XXVIII, pp 293-299, Lecture Notes in Maths 1583, Springer Verlag, 1994

21.       The rate function of hypoelliptic diffusions, 18 pages, with J-D Deuschel, Communications in Pure and Applied Mathematics, vol XLVII, numéro 6, pp 843-861, 1994

20.       Holder norms and the support theorem for diffusions, with Michel Ledoux and Mihai Gradinaru. Annales de l'IHP, vol 30, numéro 3, pp 415-436, 1994

19.       Normes holderiennes et support des diffusions, with Mihai Gradinaru, CRAS, tome 316, pp 282-286, 1993.

18.       Precise asymptotics in large deviations, with J-D Deuschel and Daniel Stroock, Bulletin des Sciences  Mathematiques, Volume 117, 1, pp 107-124, 1993

17.       Laplace asymptotics for reaction diffusion equations, with Alain Rouault, Probability theory and related fields, Vol 97 p 259-285, 1993

16.       Schilder's large deviation theorem without topology, with Michel Ledoux, In “Asymptotic problems in probability” pp 107-122 Pitman Research Notes, No 284. Longman Taniguchi Symposium on stochastic analysis (Kyoto 1990). Editors Elworthy and Ikeda, 1993

15.       Large deviations and Strassen theorem in Holder norm, with Pierre Baldi and Gérard Kerkyacharian, Stochastic processes and applications, 42, pp 171-190, 1992.

14.       Géométrie de la courbe brownienne plane, Séminaire Bourbaki 43ème année, 1990-1991, number 730, pp 7-42 ; Astérisque 201-202- 203, 1992

13.       Annulation plate du noyau de la chaleur hypoelliptique, with Rémi Léandre. CRAS. tome 312, Série I, pp 463-464, 1991

12.       Décroissance exponentielle du noyau de la chaleur sur la diagonale (2 ), with Rémi Léandre Probability theory and related fields, 90, pp 377-402, 1991.

11.       Décroissance exponentielle du noyau de la chaleur sur la diagonale (1), with Rémi Léandre Probability theory and related fields, 90, pp 175-202, 1991

10.       Methode de Laplace: étude variationnelle des fluctuations de diffusions de type champ moyen, with Marc Brunaud, Stochastics, vol 31, pp 79-144, 1990.

9.         Quelques remarques sur le cut-locus sous-riemannien, with Remi Léandre, "Stochastics, Algebra and Analysis in classical and quantum dynamics" Sergio Albeverio editor, Kluwer 1990

8.         Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale. Annales de l'institut Fourier, tome 39, fascicule 1, pp 73-99, 1989

7.         http://www.springerlink.com/content/p587080k28m63724/, Probability theory and related fields, Vol 81, pp 29-77, 1989

6.         Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus. Annales scientifiques de l'Ecole Normale Supérieure, 4ème série, tome 21, pp 307-331, 1988

5.         Méthode de Laplace et de la phase stationnaire sur l'espace de Wiener. Stochastics, Vol 25, p 125-153, 1988

4.         Noyau de la chaleur hypoelliptique et géométrie sous-riemannienne. Colloque Franco-Japonais de Probabilités. Stochastic Analysis, éditeurs Michel Métivier and Sumio Watanabe, Lecture Notes in Maths 1322, p 1-16, Springer-Verlag, 1987

3.         The Poisson Kernel for certain degenerate elliptic operators (avec Daniel Stroock and Shigeo Kusuoka) Journal of Functional Analysis. Vol 56, p 171-208, 1984

2.         Représentation explicite des solutions d'équations stochastiques invariantes sur un groupe de Lie. Journées SMF Nancy 1981. Institut Elie Cartan Vol 7 pp 1-10, 1983

1.         Equations stochastiques à coefficients analytiques et séries de Taylor stochastiques. Annales scientifiques de l'université de Clermont-Ferrand pp 55-69, 1982