Photo of Gérard Ben Arous

Gérard BEN AROUS

Courant Institute of Mathematical Sciences
New York University

Professor of Mathematics

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




Biography

Curriculum Vitae

Department of Mathematics
Courant Institute
New York University

Publications

  1. Spectral gap estimates for Spin Glasses, with A. Jagannath, Submitted, Arxiv:1705.04243, 2017
  2. Exact asymptotics and stable laws for branching random walks in random environments, with S. Molchanov, A. Ramirez, Submitted, 2017
  3. Scaling limits for random walks on critical clusters on trees, with A. Fribergh, M. Cabezas, Submitted, Arxiv:1705.05883, 2017
  4. Scaling limit for the ant in a simple labyrinth, with A. Fribergh, M. Cabezas, Submitted, Arxiv:1609.03980, 2016
  5. Scaling limit for the ant in high dimensional labyrinths, with A. Fribergh, M. Cabezas, Submitted, Arxiv:1609.03977, 2016
  6. Second order expansion for implied volatility in two factor local volatility models, with P. Laurence, In: Large Deviations and Asymptotic methods in finance, pp 89-136, Springer Proceedings in Mathematics and Statistics, Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, J. Teichman, Springer-Verlag, 2016
  7. Biased Random Walks on Random Graphs, with A. Fribergh Proceedings of Symposia in Pure Mathematics, Vol 91, pp 99-155, AMS, 2016. “Probability and Statistics in St-Petersburg, Editors V. Sidoravicius and S. Smirnov.
  8. Explorations on high dimensional landscapes, with L. Sagun, V. Ugur Guney, and Yann Le Cun International Conference on learning representations, ICLR 2015
  9. The landscape of the loss surface of multilayer networks, with A. Choromanska, Yann Le Cun, in Conference on learning theory, COLT 2015, JMLR, Vol 40:1-5, 2015
  10. The loss surface of multilayer networks, with A. Choromanska, M. Henaff, M. Mathieu, and Yann Le Cun, Conference on Artificial Intelligence and Statistics, (AISTATS) 2015
  11. Randomly Trapped Random Walks, with M. Cabezas, J. Cerny, R. Royfman, Annals of Probability, Vol 43, No. 5, 2405-2457, 2015
  12. On fluctuations of eigenvalues of random permutation matrices, with K. Dang, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, Vol 51, No. 2, 620-647, 2015
  13. Topics in percolative and disordered systems, with A. Ramirez, P. Ferrari, C. Newman, V. Sidoravicius, P. Ferrari, ME. Vares. Springer Proceedings in Mathematics and Statistics, Vol 69, Springer Verlag, 2014
  14. A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases, with A. Fribergh and V. Sidoravicius, CPAM, Volume 67, no. 4, pp 519-530, 2014
  15. A Central Limit theorem in many body Quantum dynamics, with K. Kirkpatrick and B. Schlein, CMP, Volume 321, no. 2, pp 371-417, 2013
  16. Complexity of random Smooth functions of many variables, with A. Auffinger, Annals of Probability, Volume 41, no. 6, pp 4214-4247, 2013
  17. Random Matrices and Complexity of Spin Glasses, with A. Auffinger and J. Cerny, CPAM, Volume 66, no. 2, pp 165-201, 2013
  18. Einstein relation for biased random walks on Galton-Watson trees, with Y. Hu, S. Olla and O. Zeitouni, Annales de l’Institut Henri Poincaré, Volume 49, no. 3, pp 698-721, 2013
  19. Extreme gaps between eigenvalues of random matrices, with Paul Bourgade, Annals of Probability, Volume 41, no. 4, pp 2648-2681, 2013
  20. Universality and extremal aging for dynamics of Spin Glasses on subexponential time scales, with Onur Gun, CPAM, volume 65, No1, pp 77-127, 2012
  21. Randomly biased walks on subcritical trees, with Alan Hammond, CPAM, Volume 65, no. 11, pp 1481-1527, 2012
  22. Biased random walks on Galton-Watson trees with leaves, with Alexander Fribergh, Nina Gantert, Alan Hammond, Annals of Probability, volume 40, no. 1, pp 280-338, 2012
  23. Current Fluctuations for TASEP, a proof of the Praehofer Spohn conjecture, with Ivan Corwin, Annals of Probability, vol 39, no. 1, 104-138, 2011
  24. Wigner Matrices, with Alice Guionnet, pp 433-451, Chapter 21 in “Handbook on Random Matrices”, edited by G. Ackemann, J. Baik, P. Di Francesco, Oxford University Press, 2010
  25. Free point-processes and free extreme values, with V. Kargin, Probability Theory and Related Fields, volume 147, No 1-2, pp 161-183, 2010
  26. Poisson convergence for the largest eigenvalues of heavy-tailed random matrices, with A.C. Auffinger and Sandrine Peche, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 45, No. 3, pp 589–610, 2009
  27. REM Universality for Random Hamiltonians, with Alexey Kuptsov, Progress in Probability, Vol. 62, pp 45–84, Birkhauser Verlag, Basel, Switzerland, 2009
  28. Universality of the REM for dynamics of mean-field spin glasses, with Anton Bovier and Jiri Cerny, Communications in Mathematical Physics, vol 282, pp. 633—695, 2008
  29. Heavy Tailed Wigner Matrices, with Alice Guionnet, Communications in Mathematical Physics, Volume 278, Number 3, pp 715-751, 2008
  30. Universality of Random Energy Model like aging in mean field spin glasses, with Anton Bovier and Jiri Cerny, Journal of Statistical Mechanics: Theory and Experiment, No. 4, L04003, 2008.
  31. A new REM conjecture, With V. Gayrard and A. Kuptsov, In and Out of Equilibrium, editors V. Sidoravicius and M.E. Vares, Progress in Probability, Birkhauser, Volume 60, pp 59-96, 2008
  32. Elementary Potential theory on the hypercube, with V. Gayrard, Electronic Journal of Probability, Volume 13, pp 1726-1807, 2008
  33. The Arcsine Law as a universal aging scheme for Trap models, with J. Cerny, Communications in Pure and Applied Mathematics, vol 61, No 3, pp 289-329, 2008.
  34. 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
  35. Scaling limits for trap models on Z^d, with J. Cerny, The Annals of Probability. Volume 35, Number 6, pp 2356-2384, 2007.
  36. Transition asymptotics for reaction-diffusion in random media, with A. Ramirez and S. 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
  37. Dynamics of Trap Models, with J. Cerny, in Mathematical Statistical Physics Lecture Notes, Vol LXXXIII Les Houches Summer School, Elsevier, 2006
  38. Cugliandolo-Kurchan Equations for dynamics of Spin Glasses, with A. Dembo and A. Guionnet, Probability Theory and Related Fields, vol 136, n°4, pp 619-660, 2006
  39. Extreme Values In Free Probability, with Dan Voiculescu, Annals of Probability, vol 34, n°5, pp 2037-2059, 2006
  40. Aging for Bouchaud’s trap model in dimension 2, with J. Cerny and T. Mountford, Probability Theory and Related Fields, vol 134, n°1, pp 1-43, 2006
  41. Phase transition for the largest eigenvalue of large sample covariance matrices, with J. Baik and S. Peche Annals of Probability vol 33, n° 5, pp 1643-1697, 2005
  42. Universality of local eigenvalue statistics for sample covariance matrices, with S. Peché, Communications of Pure and Applied Mathematics, vol 58, n°10, pp 1316-1357, 2005
  43. Bouchaud model exhibits two aging regimes in dimension 1, with J. Cerny, Annals of Applied Probability vol 15, n°2, pp 1161-1192, 2005.
  44. Limit Laws for Sums of Random Exponentials, with L. Bogatchev and S. Molchanov, Probability Theory and Related Fields, vol 132, n°4, pp 579-612, 2005
  45. Transition from the annealed to the quenched asymptotics for random walkson random obstacles, with S. Molchanov and A. Ramirez, Annals of Probability, vol 33, n° 6, pp 2149-2187, 2005
  46. Limit Laws for Sums of Random Exponentials, with L. Bogatchev and S. Molchanov, Recent developments in Stochastic Analysis and related topics, pp 45-65, World Scientific, Hackensack, NJ, 2004
  47. Algorithms for Stochastic Approximations of Curvature Flows, with G. Unal, D. Nain, N. Shimkin, A. Tannenbaum and O. Zeitouni, Proceedings of ICIP, 2004
  48. Spatio-temporal large deviations principle for coupled circle maps, with J.B. Bardet, Annals of Probability, vol 32 n°1, pp 692-729, 2004.
  49. Large Deviations in the Langevin dynamics of a short range spin glass, with M. Sortais, Bernoulli, vol 9 n°6, pp 921-954, 2003.
  50. A two armed-bandit type problem, with M. Benaim, International Journal of Game Theory, vol 32, pp 3-16, 2003.
  51. 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.
  52. Internal DLA in a random environment, with J. Quastel and A:Ramirez, Annales de l’Institut Henri Poincaré, vol 39 n°2, pp 301-324, 2003
  53. Glauber dynamics of the random energy model. II. Aging below the critical temperature, with A. Bovier and V. Gayrard, Communications in Mathematical Physics, vol 236 n°1, pp1-54, 2003
  54. Glauber dynamics of the random energy model. I. Metastable motion on the extreme states, with A. Bovier and V. Gayrard, Communications in Mathematical Physics, vol 235 n°3, pp 379-425, 2003
  55. Large deviations in the Langevin dynamics of a random field Ising model, with M. Sortais, Stochastic Processes and Applications, vol 105 n°2, pp 211-255, 2003
  56. Crystalline Stochastic Systems and curvature driven flows, with A. Tannenbaum and O. Zeitouni. pp 41-63, Mathematical Systems theory in Biology, Communications and Finance, IMA volume in Mathematics and its Applications 134, Springer, New York 2003. Editors J. Rosenthal and D. Gilliam.
  57. Stochastic approximations to curve-shortening flows via particle systems, with A. Tannenbaum and O. Zeitouni. Journal of Differential Equations, vol 195 n°1, pp 119-142, 2003.
  58. Aging and spin-glass dynamics. Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), pp 3-14, Higher Ed. Press, Beijing, 2002.
  59. Phase transition for the spherical hierarchical model, with O. Hryniv and S. Molchanov, Markov Processes and Related Fields, vol 8 n°4, pp 565-594, 2002.
  60. Aging in the Random Energy Model, with A. Bovier and V. Gayrard, Vol 8, issue 88, Phys. Rev Letters, 2002
  61. Super-diffusivity in a shear flow model from perpetual homogenization, with H. Owhadi, Communications in Mathematical Physics, vol 227 n°2, pp 281-302, 2002.
  62. The canonical equation of adaptive dynamics: a mathematical view, with N. Champagnat and R. Ferriere, Selection, vol 2, pp 71-81, 2001.
  63. Aging of spherical spin glasses, with A. Dembo and A. Guionnet, Probability Theory and Related Fields, Vol 120 no 1, pp 1-67, 2001.
  64. Growth and saturation in random media, with A. Ramirez. Stochastic processes, physics and geometry: new interplays, 41--54, CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000.
  65. Asymptotic survival probabilities in the random saturation process, with A. Ramirez, The Annals of Probability, Vol 28, no. 4, pp 1470—1527, 2000.
  66. Large deviations of Brownian motion on the Sierpinski gasket, with T. Kumagai, Stochastic Process and Applications, Vol 85 no. 2, pp 225—235, 2000.
  67. Quenched asymptotics for survival probabilities in the random saturation process, with A. Ramirez, C.R. Acad. Sci. Paris, p. 1003-1008, 1999.
  68. Increasing propagation of chaos for mean field models, with O. Zeitouni, Annales de l'IHP, vol 35, pp85-102, 1999.
  69. Large deviations from the circular law, with O. Zeitouni, ESAIM: Probability and Statistics, Vol. 2, pp. 123-134, 1998. http://www.emath.fr/emath/Maths/Ps/ps.html
  70. Singularity of hypoelliptic Green functions, with M. Gradinaru. Potential Analysis and Applications, vol 8, pp 217-258, 1998.
  71. Langevin Dynamics for Sherrington-Kirkpatrick Spin Glasses, avec A. Guionnet, chapter of the book: "Mathematical Aspects of Spin Glasses and Neural Networks ", pp. 321-353, Progress in Probability no 41, Birkhauser, 1998.
  72. Symmetric Langevin Spin Glass Dynamics, with A. Guionnet, Annals of Probability, vol. 25, No 3, pp1367-1422, 1997.
  73. Large deviations for Wigner's law and Voiculescu's non commutative entropy, with A. Guionnet, Probability theory and related fields, volume 108, 4, pp 517-542, 1997.
  74. Singularités des fonctions de Green hypoelliptiques, with M. Gradinaru, Annales Mathématiques Blaise Pascal, vol 3, 1996.
  75. Metastability for dynamics of the 3D Ising model, with R. Cerf. Electronic Journal in Probability, vol 1, 1996.
  76. The Construction of the d-dimensional Gaussian Droplet, with J.D. Deuschel, Communications in Math. Physics, vol 179, pp 467-488, 1996.
  77. A probabilistic approach to semi-classical approximations, with F. Castell, Journal of Functional Analysis, vol 137, pp 243-280, 1996.
  78. Flow Decomposition and Large Deviations, with F. Castell, Journal of Functional Analysis, vol 140, pp 23-67, 1996.
  79. Large deviations for Langevin Spin Glass Dynamics, with A. Guionnet. Probability theory and related fields, 102, pp 455-509, 1995.
  80. Coupling constructions for hypoelliptic diffusions, with M. Cranston and W. Kendall. Proceedings of Symposia in Pure mathematics, AMS, 1994, pp 193-213, 1994.
  81. Grandes déviations de Freidlin-Wentzell en norme holderienne, with M. Ledoux. Séminaire de Probabilités XXVIII, pp 293-299, Lecture Notes in Maths 1583, Springer Verlag, 1994.
  82. 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.
  83. Holder norms and the support theorem for diffusions, with M. Ledoux and M. Gradinaru. Annales de l'IHP, vol 30, numéro 3, pp 415-436, 1994.
  84. Normes holderiennes et support des diffusions, with M. Gradinaru, CRAS, tome 316, pp 282-286, 1993.
  85. Precise asymptotics in large deviations, with J.D Deuschel and D. Stroock, Bulletin des Sciences Mathematiques, Volume 117, 1, pp 107-124, 1993.
  86. Laplace asymptotics for reaction diffusion equations, with A. Rouault. Probability theory and related fields, Vol 97 p 259-285, 1993.
  87. Schilder's large deviation theorem without topology, with M. Ledoux. In “Asymptotic problems in probability” pp 107-122 Pitman Research Notes numéro 284.Longman 1993. Taniguchi Symposium on stochastic analysis (Kyoto 1990). Editors Elworthy and Ikeda.
  88. Large deviations and Strassen theorem in Holder norm, with P. Baldi and G. Kerkyacharian. Stochastic processes and applications, 42, pp 171-190, 1992.
  89. Géométrie de la courbe brownienne plane, Séminaire Bourbaki 43ème année, 1990-1991, number 730, pp 7-42 ; Astérisque 201-202- 203, 1992.
  90. Annulation plate du noyau de la chaleur hypoelliptique, with Rémi Léandre. CRAS. tome 312, Série I, pp 463-464, 1991.
  91. Décroissance exponentielle du noyau de la chaleur sur la diagonale (2), with Rémi Léandre Probability theory and related fields, 90, pp 377-402, 1991.
  92. Décroissance exponentielle du noyau de la chaleur sur la diagonale (1), with Rémi Léandre Probability theory and related fields, 90, pp 175-202, 1991.
  93. Methode de Laplace : étude variationnelle des fluctuations de diffusions de type champ moyen, with Marc Brunaud. Stochastics, vol 31, pp 79-144, 1990.
  94. Quelques remarques sur le cut-locus sous-riemannien, with Remi Léandre, "Stochastics, Algebra and Analysis in classical and quantum dynamics" S. Albeverio editor, Kluwer 1990.
  95. Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale. Annales de l'institut Fourier, tome 39, fascicule 1, pp 73-99, 1989.
  96. Flots et séries de Taylor stochastiques. Probability theory and related fields, Vol 81, pp 29-77, 1989.
  97. 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.
  98. Méthode de Laplace et de la phase stationnaire sur l'espace de Wiener. Stochastics, Vol 25, p 125-153, 1988.
  99. Noyau de la chaleur hypoelliptique et géométrie sous-riemannienne. Colloque Franco-Japonais de Probabilités. Stochastic Analysis, éditeurs M. Metivier and S. Watanabe, Lecture Notes in Maths 1322, 1987, p 1-16, Springer-Verlag.
  100. The Poisson Kernel for certain degenerate elliptic operators (avec D.W. Stroock and S. Kusuoka) Journal of Functional Analysis. Vol 56, p 171-208, 1984.
  101. 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.
  102. Equations stochastiques à coefficients analytiques et séries de Taylor stochastiques. Annales scientifiques de l'université de Clermont-Ferrand pp 55-69, 1982.