Department of Mathematics

Search

List of publications

Books and monographs

  1. Topics in propagation of chaos, course given at the Saint-Flour Probability Summer School, 1989. Lecture Notes in Math. 1464, Springer, Berlin, 164-251, 1991.
  2. Brownian motion, obstacles and random media, Springer, Berlin, 1998.
  3. with E. Bolthausen: Ten lectures on Random Media, DMV-Lectures, vol. 32, Birkhäuser, Basel, 2002.
  4. Topics in random walks in random environment, in: School and Conference on Probability Theory, ICTP Lecture Notes Series, Trieste, 17, 203-266, 2004.
  5. Topics in occupation times and Gaussian free fields, Notes of the course "Special topics in probability", Spring 2012, Zurich Lectures in Advanced Mathematics, EMS, Zurich.

Articles

  1. Modèles stationnaires de files d'attente, C. R. Acad. Sci. Paris, t. 286, Série A. 563-566, 1978.
  2. Perturbations Ponctuelles d'évolutions: construction d'espaces stationnaires, Ann. Inst. Henri Poincaré, Nouv. Série Sect. B, 16, 4, 299-326, 1980.
  3. Martingales dépendant d'un paramètre: une formule d'Ito, C. R. Acad. Sci., Paris, t. 293, Série I, 431-434, 1981.
  4. with P. L. Lions, and J. L. Menaldi: Construction de processus de diffusions réfléchis par pénalisation du domaine, C. R. Acad. Sci., Paris, t. 292, Série I, 559-562, 1980.
  5. Minimal length multi-channel, Ann. Inst. Henri Poincaré, Nouv. Série Sect. B, 18, 1, 103-114, 1982.
  6. Martingales dépendant d'un paramètre: une formule d'Ito, Z. Warscheinlichkeitstheorie verw. Gebiete, 60, 41-70, 1982.
  7. Equations de type Boltzmann, spatialement homogènes, C. R. Acad. Sci. Paris, t. 295, Série I, 363-366, 1982.
  8. with P. E. Protter: An equation involving local time, Séminaire de Probabilités XVII, Lect. Notes in Mathematics, 986, 62-66, 1983.
  9. Nonlinear reflecting diffusion process and the propagation of chaos and associated fluctuations, J. Funct. Anal., 56, 3, 311-336, 1984.
  10. Equations de type Boltzmann spatialement homogènes, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 66, 559-592, 1984.
  11. with P. L. Lions: Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37, 4, 511-537, 1984.
  12. A fluctuation result for nonlinear diffusions, in Infinite Dimensional Analysis and Stochastic Processes, S. Albeverio editor, Pitman, Boston, 145-160, 1985.
  13. with S.R.S. Varadhan: A multidimensional process involving local time, Probab. Theory Relat. Fields, 71, 553-579, 1986.
  14. A propagation of chaos result for Burger's equation, Probab. Theory Relat. Fields, 71, 581-613, 1986.
  15. with P. March: Some connections between excursion theory and the discrete Schrödinger equation with random potentials, Probab. Theory Relat. Fields, 75, 11-53, 1987.
  16. A propagation of chaos result for Burger's equation, Proc. IMA volumes, G. Papanicolaou editor, vol. 9, Hydrodynamic behavior and interacting particle systems, Springer, New York, 181-188, 1987.
  17. Some bounds and limiting results for the measure of the Wiener sausage of small radius associated to elliptic diffusions, Stoch. Proc. and Appl., 25, 1-25, 1987.
  18. Propagation of chaos for a system of annihilating Brownian spheres, Comm. Pure Appl. Math., 60, 663-690, 1987.
  19. Grandes déviations, Séminaire Bourbaki, 39ème année, 1986-87, no. 680, Feb. 1987, Astérisque, Paris, 152-153, 207-227, 1988.
  20. A limiting result for the structure of collisions between many independent diffusions, Probab. Theory Relat. Fields, 81, 353-381, 1989.
  21. A trajectorial representation for certain local nonlinear equations, Proc. Coll. P. Lévy, Astérisque, Paris 157-158, 363-370, 1988.
  22. Lifschitz tail and Wiener sausage on hyperbolic space, Comm. Pure Appl. Math., 42, 1033-1065, 1989.
  23. Lifschitz tail on hyperbolic space: Neumann conditions, Comm. Pure Appl. Math., 43, 1-30, 1990.
  24. Singularité de Lifschitz et saucisse de Wiener sur l'espace hyperbolique, C. R. Acad. Sci., Paris, t. 307, Série I, 843-845, 1988.
  25. Lifschitz tail and Wiener sausage I, J. Funct. Anal., 94, 223-246, 1990.
  26. Lifschitz tail and Wiener sausage II, J. Funct. Anal., 94, 247-272, 1990.
  27. Long time asymptotics for the shrinking Wiener sausage, Comm. Pure Appl. Math., 43, 809-820, 1990.
  28. On the confinement property of two dimensional Brownian motion among Poissonian obstacles, Comm. Pure Appl. Math., 44, 1137-1170, 1991.
  29. On long excursions of Brownian motion among Poissonian obstacles, stochastic analysis, M. Barlow, N. Bingham editors, London Math. Soc. Lecture Note Series, Cambridge University Press, 353-375, 1991.
  30. Brownian survival among Gibbsian traps, Ann. Probab., 21, 1, 490-509, 1993.
  31. Brownian asymptotics in a Poissonian environment, Probab. Theory Relat. Fields, 95, 155-174, 1993.
  32. Brownian motion in a Poissonian potential, Probab. Theory Relat. Fields, 97, 447-477, 1993.
  33. Brownian motion with a drift in a Poissonian potential, Comm. Pure Appl. Math., 47, 1283-1318, 1994.
  34. Brownian motion and obstacles, First European Congress of Mathematics, vol. I, Birkhäuser, Basel, 225-248, 1994.
  35. Shape theorem, Lyapounov exponents, and large deviations for Brownian motion in a Poissonian potential, Comm. Pure Appl. Math., 47, 1655-1688, 1994.
  36. Annealed Lyapounov exponents and large deviations in a Poissonian potential I, Ann. Scient. de l'Ecole Normale Supérieure, 4ème série, 28, 345-370, 1995.
  37. Annealed Lyapounov exponents and large deviations in a Poissonian potential II, Ann. Scient. de l'Ecole Normale Supérieure, 4ème série, 28, 371-390, 1995.
  38. Some aspects of Brownian motion in a Poissonian potential, 137-143, Proceedings Symposia in Pure Mathematics, M. Cranston, M. Pinsky editors, A.M.S., Providence, 57, 137-143, 1995.
  39. Quenched critical large deviations for Brownian motion in a Poissonian potential, J. Funct. Anal., 131, 1, 54-77, 1995.
  40. Crossing velocities and random lattice animals, Ann. Probab., 23, 3, 1006-1023, 1995.
  41. Brownian confinement and pinning in a Poissonian potential I, Probab. Theory Relat. Fields, 105, 1-29, 1996.
  42. Brownian confinement and pinning in a Poissonian potential II, Probab. Theory Relat. Fields, 105, 31-56, 1996.
  43. Distance fluctuations and Lyapounov coefficients, Ann. Probab., 24, 3, 1507-1530, 1996.
  44. Capacity and principal eigenvalues: the method of enlargement of obstacles revisited, Ann. Probab., 25, 3, 1180-1209, 1997.
  45. Fluctuations of principal eigenvalues and random scales, Commun. Math. Phys., 189, 337-363, 1997.
  46. with Y. Le Jan: Cascades aléatoires et équations de Navier-Stokes, C.R. Acad. Sci., Paris, t.324, Série I, 823-826, 1997.
  47. with Y. Le Jan: Stochastic cascades and 3-dimensional Navier Stokes equations, Prob. Theory Relat. Fields, 109, 343-366, 1997.
  48. with E. Bolthausen: On Ruelle's probability cascades and an abstract cavity methods, Commun. Math. Phys., 197, 247-276, 1998.
  49. Slowdown and neutral pockets for a random walk in random environment, Probab. Theory Relat. Fields, 115, 287-323, 1999.
  50. Brownian motion and random obstacles, in Proceedings International Congress of Mathematicians, Berlin 1998, Documenta Mathematica, vol. III, 301-310, 1998.
  51. with M.P.W. Zerner: A law of large numbers for random walks in random environment, Ann. Probab., 27, 4, 1851-1869, 1999.
  52. Slowdown and central limit theorem for random walks in random environment, J. Eur. Math. Soc., 2, 93-143, 2000.
  53. On a class of transient random walks in random environment, Ann. Probab., 29, 2, 723-764, 2001.
  54. An effective criterion for ballistic behavior of random walks in random environment, Probab. Theory Relat. Fields, 122, 4, 509-544, 2002.
  55. with E. Bolthausen: On the static and dynamic points of views for certain random walks in random environment, Methods and Applications of Analysis, 9, 3, 345-376, 2002.
  56. Milieux aléatoires et petites valeurs propres, Etats de la Recherche, Luminy, Nov. 2000, Panorama et Synthèses, SMF, 12, 13-36, 2001.
  57. On new examples of ballistic random walks in random environment, Ann. Probab., 31, 1, 285-322, 2003.
  58. with E. Bolthausen and O. Zeitouni: Cut points and diffusive random walks in random environment, Ann. I. H. Poincaré - PR 39, 527-555, 2003.
  59. On the anisotropic walk on the supercritical percolation cluster, Commun. Math. Phys, 240, 123-148, 2003.
  60. with V. Sidoravicius: Quenched invariance principles for walks on clusters of percolation or among random conductances, Probab. Theory Relat. Fields, 129, 2, 219-244, 2004.
  61. with O. Zeitouni: On the diffusive behavior of isotropic diffusions in a random environment, C.R. Acad. Sci. Paris, Ser. I 339, 429-434, 2004.
  62. with O. Zeitouni: An invariance principle for isotropic diffusions in random environment, Inventiones Mathematicae, 164, 3, 455-567, 2006.
  63. with A. Dembo: On the disconnection of a discrete cylinder by a random walk, Probab. Theory Relat. Fields, 136, 2, 321-340, 2006.
  64. Random motions in random media, in Mathematical Statistical Physics, A. Bovier, F. Dunlop, F. den Hollander, A. van Enter and J. Dalibard, eds., Les Houches, Session LXXXIII, 2005, Elsevier, 219-242, 2006.
  65. How universal are asymptotics of disconnection times in discrete cylinders? Ann. Probab., 36, 1, 1-53, 2008.
  66. with I. Benjamini: Giant component and vacant set for random walk on a discrete torus, J. Eur. Math. Soc., 10, 1, 1-40, 2008.
  67. with A. Dembo: A lower bound on the disconnection time of a discrete cylinder, Progress in Probability, vol. 60, In and Out of Equilibrium 2, Birkhäuser, Basel, 211-227, 2008.
  68. Vacant set of random interlacements and percolation, Ann. Math., 171, 2039-2087, 2010.
  69. Random walks on discrete cylinders and random interlacements, Probab. Theory Relat. Fields, 145, 143-174, 2009.
  70. with E. Bolthausen: Zur Verleihung des Abel-Preises 2007 an Srinisava S.R. Varadhan, Mitteilungen der DMV, 15, 31-33, 2007.
  71. Upper bound on the disconnection time of discrete cylinders and random interlacements, Annals of Probability, 37, 5, 1715-1746, 2009.
  72. with V. Sidoravicius: Percolation for the vacant set of random interlacements, Comm. Pure Appl. Math., 62, 6, 831-858, 2009.
  73. On the domination of random walk on a discrete cylinder by random interlacements, Electron. J. Probab., 14, 1670-1704, 2009.
  74. with V. Sidoravicius: Connectivity bounds for the vacant set of random interlacements, Ann. Inst. Henri Poincaré, Probabilités et Statistiques, 46, 4, 976-990, 2010.
  75. A lower bound on the critical parameter of interlacement percolation in high dimension, Probab. Theory Relat. Fields, 150, 575-611, 2011.
  76. On the critical parameter of interlacement percolation in high dimension, Ann. Probab., 39, 1, 70-103, 2011.
  77. Decoupling inequalities and interlacement percolation on G x Z, Inventiones mathematicae, 187, 3, 645-706, 2012.
  78. Random interlacements and the Gaussian free field, Ann. Probab., 40, 6, 2400–2438, 2012.
  79. On (Z/NZ)^2-occupation times, the Gaussian free field, and random interlacements, Bull. Inst. Math. Acad. Sin. (N.S.), 7, 4, 565-602, 2012; in honor of the 70th Birthday of Prof. S.R.S. Varadhan.
  80. An isomorphism theorem for random interlacements, Electron. Commun. Probab., 17, 9, 1-9, 2012.
  81. S.R.S. Varadhan: National Medal of Science, IMS Bulletin, 40, 8, 6-7, 2011.
  82. with P.-F. Rodriguez: Phase transition and level-set percolation for the Gaussian free field, Commun. Math. Phys., 320, 571-601, 2013.
  83. On scaling limits and Brownian interlacements. Bull. Braz. Math. Soc., New Series 44(4), 555-592, 2013. Special issue of the Bulletin of the Brazilian Mathematical Society-IMPA 60 years.
  84. with X. Li: Large deviations for occupation time profiles of random interlacements, Probab. Theory Relat. Fields, 161, 309-350, 2015.
  85. with X. Li: A lower bound for disconnection by random interlacements, Electron. J. Probab., 19, 17, 1-26, 2014.
  86. Disconnection and level-set percolation for the Gaussian free field, J. Math. Soc. Japan, 67, 1801-1843, 2015; special issue on the centennial of the birth of Kiyosi Itô.
  87. Coupling and an application to level-set percolation of the Gaussian free field, Electron. J. Probab., 21, 35, 1–26, 2016.
  88. Disconnection, random walks and random interlacements, Probab. Theor. Relat. Fields, 167, 1-2, 1-44, 2017.
  89. with A. Abächerli: Level-set percolation for the Gaussian free field on a transient tree, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 54, 1, 173-201, 2018.
  90. with M. Nitzschner: Solidification of porous interfaces and disconnection, J. Eur. Math. Soc., 22, 2629-2672, 2020.
  91. On macroscopic holes in some supercritical strongly dependent percolation models, Ann. Probab., 47, 4, 2459-2493, 2019.
  92. On coupling and "vacant set level set" percolation. Electron. Commun. Probab., 24, 20, 1-12, 2019.
  93. On bulk deviations for the local behavior of random interlacements. Ann. Scient. Éc. Norm. Sup., série 4, t. 56, 801-858, 2023.
  94. On the C^1-property of the percolation function of random interlacements and a related variational problem. In In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, M.E. Vares, R. Fernandez, L.R. Fontes, C.M. Newman (eds.), pp. 775-796, Birkhäuser, 2021.
  95. Excess deviations for points disconnected by random interlacements. Probability and Mathematical Physics, 2-3, 563–611, 2021.
  96. On the cost of the bubble set for random interlacements. Inventiones mathematicae, 233, 2, 903-950, 2023.
  97. On the spectral gap in the Kac-Luttinger model and Bose-Einstein condensation. Appeared in the special issue "A tribute to Francis Comets" of Stochastic Process. Appl. 166 (2023), 104197.
JavaScript has been disabled in your browser