The intersection of probability and physics has been a rich and explosive area of growth in the past two decades. This volume contains invited articles by leading probabilists highlighting these advances. Major areas covered include: percolation theory, random walks, interacting particle systems and topics related to statistical mechanics. Graduate students and researchers in probability theory and math physics should find this book a useful reference. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes; Wulf constructions in higher dimensions for percolation; Potts and Ising models; classification of random walks in random environments; the introduction of the stochastic Loewner equation; the rigorous proof of intersection exponents for planar Brownian motion; and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability.All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. The contributors are K. Alexander, J. van den Berg, T. Bodineau, F. Camia, N. Cancrini, G. Grimmett, P. Hiemer, A.E. Holroyd, H. Kesten, G.F. Lawler, T.M. Liggett, J. Lorinczi, F. Martinelli, C.M. Newman, J. Quastel, C.-E. Pfister, M. Prahofer, C. Roberto, O. Schramm, V. Sidoravicius, H. Spohn, A. Toom, B. Toth, D. Ueltschi, W. Werner, M. Wschebor and M. Wuthrich.
