zbMATH — the first resource for mathematics

Brownian motion in a Poisson obstacle field. (English) Zbl 0964.60091
Séminaire Bourbaki. Volume 1998/99. Exposés 850-864. Paris: Société Mathématique de France, Astérisque. 266, 91-111, Exp. No. 853 (2000).
The paper is devoted to the problem of a diffusion performed in medium with randomly distributed static traps. The structure of the paper is as follows. In the first four sections the author gives a brief survey on some of the results available in the area. For example, in Section 2 he shows, that on the average the behavior of the survival probability \(S_t\) of the particle in the field up to time \(t\), the so-called annealed asymptotic, is given by \[ S_t=\exp\{-\tilde{c}(d,\nu)t^{d/(d+2)}(1+o(1))\}, \quad t\gg 1, \] where \(\nu\) is the intensity of the Poisson cloud and \(\tilde{c}(d,\nu)\) is a constant given in explicit form. Section 6 presents the main ingredients of MEO, which is crucial in the theory. The author closes the article with a short review of some open problems in the subject.
For the entire collection see [Zbl 0939.00019].

60K40 Other physical applications of random processes
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
Full Text: Numdam EuDML