Course Identification

Analysis (at the level of basic topics), probability theory.

The course will focus on the analysis of random walks on the d-dimensional lattice, when

The transition probabilities are random, space-dependent, and time independent. Basic tools will be described: electrical networks (for d=1), homogenization and the environment viewed from the point of view of the particle, regeneration times and their relation to the central limit theorem, and perturbative methods.

Zeitouni, O., Random walks in random environment, XXXI Summer school in probability ,St Flour (2001). Lecture notes in Math. 1837 (Springer 2004, pp. 193--312).

T. Komorowski, C. Landim, S. Olla,  Fluctuations in Markov Processes, Springer, 2012

Upon successful completion of the course students will be able to:

[1] Demonstrate understanding of homogenization theory and of the tools needed to study motion in random media.