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Milieux aléatoires
 
Nina Gantert Universität Karlsruhe, Karlsruhe, Germany
Josselin Garnier Université Paul Sabatier, Toulouse, France
Stefano Olla Université de Paris 9-Dauphine, Paris, France
Zhan Shi Université de Paris VI, Paris, France
Alain-Sol Sznitman Mathematik, ETH-Zentrum, Zürich, Switzerland
A publication of the Société Mathématique de France
Milieux aleatoires
Softcover ISBN:  978-2-85629-127-6
Product Code:  PASY/12
List Price: $33.00
AMS Member Price: $26.40
Please note AMS points can not be used for this product
Milieux aleatoires
Click above image for expanded view
Milieux aléatoires
Nina Gantert Universität Karlsruhe, Karlsruhe, Germany
Josselin Garnier Université Paul Sabatier, Toulouse, France
Stefano Olla Université de Paris 9-Dauphine, Paris, France
Zhan Shi Université de Paris VI, Paris, France
Alain-Sol Sznitman Mathematik, ETH-Zentrum, Zürich, Switzerland
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-127-6
Product Code:  PASY/12
List Price: $33.00
AMS Member Price: $26.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    Panoramas et Synthèses
    Volume: 122002; 159 pp
    MSC: Primary 60; 82;

    Random media are natural models for nonhomogeneous materials which possess some kind of statistical regularity. The study of stochastic processes in random media is currently an active field of research, and new techniques have recently been developed, including mathematical forms of renormalization. Those techniques apply to models which are much more delicate than exactly soluble ones or even reversible ones.

    The session, “États de la Recherche”, presented the state of the art in the field and brought it to a large portion of the scientific community. Based on the notes of the courses delivered during the session, this volume is composed of five articles and a general introduction, where all basic notions from probability theory are defined. The introduction and the style of the articles make the volume readable by nonspecialists.

    The article by Alain Sznitman studies the survival of Brownian motion moving among randomly located obstacles, and the ballistic behavior of the random walk in random media on the \(d\ge 2\)-dimensional lattice. This illustrates the role of atypical pockets in the medium and of abnormally small eigenvalues. The second article, by Zhan Shi, presents the analysis via stochastic calculus of Sinaï's random walk and of the one dimensional diffusion in a Brownian potential. Nina Gantert studies the random walk on a random Galton-Watson tree, in particular, the probability of rare events. Stefano Olla studies random homogenization, taking the point of view of the environment seen from the particle, as well as applications to interacting particle systems. In the last article, Josselin Garnier studies wave propagation in random media, the competition between nonlinear and random effects, and solitons in this framework.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 122002; 159 pp
MSC: Primary 60; 82;

Random media are natural models for nonhomogeneous materials which possess some kind of statistical regularity. The study of stochastic processes in random media is currently an active field of research, and new techniques have recently been developed, including mathematical forms of renormalization. Those techniques apply to models which are much more delicate than exactly soluble ones or even reversible ones.

The session, “États de la Recherche”, presented the state of the art in the field and brought it to a large portion of the scientific community. Based on the notes of the courses delivered during the session, this volume is composed of five articles and a general introduction, where all basic notions from probability theory are defined. The introduction and the style of the articles make the volume readable by nonspecialists.

The article by Alain Sznitman studies the survival of Brownian motion moving among randomly located obstacles, and the ballistic behavior of the random walk in random media on the \(d\ge 2\)-dimensional lattice. This illustrates the role of atypical pockets in the medium and of abnormally small eigenvalues. The second article, by Zhan Shi, presents the analysis via stochastic calculus of Sinaï's random walk and of the one dimensional diffusion in a Brownian potential. Nina Gantert studies the random walk on a random Galton-Watson tree, in particular, the probability of rare events. Stefano Olla studies random homogenization, taking the point of view of the environment seen from the particle, as well as applications to interacting particle systems. In the last article, Josselin Garnier studies wave propagation in random media, the competition between nonlinear and random effects, and solitons in this framework.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.