Recent progress on the understanding of the Random Conductance Model is reviewed and
commented. A particular emphasis is on the results on the scaling limit of the random walk …

Random walks in random environments and their diffusion analogues have been a source
of surprising phenomena and challenging problems, especially in the non-reversible …

Suppose we immerse a large porous stone in a bucket of water. What is the probability that
the centre of the stone is wetted? In formulating a simple stochastic model for such a …

The idea of writing up a book on the hydrodynamic behavior of interacting particle systems
was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the …

This book deals with one of the fundamental problems of nonequilibrium statistical
mechanics: the explanation of large-scale dynamics (evolution differential equations) from …

Interactive Particle Systems is a branch of Probability Theory with close connections to
Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T …

Mathematics is playing an ever more important role in the physical and biological sciences,
provoking a blurring of boundaries between scienti? c disciplines and a resurgence of …

The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

These notes on random walks in random environments (RWRE) reflect what I hoped to
cover in the 15 hours of the St Flour course on this topic, July 9–25, 2001. Of course, this …

The Stokes–Einstein and Stokes–Einstein–Debye relations hold well in nonsupercooled
liquids; however, sizeable deviations from the former appear in supercooled liquids, leading …