For more than two decades percolation theory, random walks, interacting partiยญ cle systems and topics related to statistical mechanics have experienced intenยญ sive growth. In the last several years, especially remarkable progress has been made in a number of directions, such as: Wulff constructions above two dimenยญ sions for percolation, Potts and Ising models, classification of random walks in random environments, better understanding of fluctuations in two dimenยญ sional growth processes, the introduction and remarkable uses of the Stochastic Loewner Equation, the rigorous derivation of exact intersection exponents for planar Brownian motion, and finally, the proof of conformal invariance for critยญ ical percolation scaling limits on the triangular lattice. It was thus a fortuitous time to bring together researchers, including many personally responsible for these advances, in the framework of the IVth Brazilian School of Probability, held at Mambucaba on August 14-19,2000. This School, first envisioned and organized by IMPA's probability group in 1997, has since developed into an annual meeting with an almost constant format: it usually offers three advanced courses delivered by prominent scientists, combined with a high-level conference. This volume contains invited articles associated with that meeting, and we hope it will provide the reader with an accurate impression regarding the current state of affairs in these important fields of probability theory
CONTENT
Randomly Coalescing Random Walk in Dimension ? 3 -- The Single Droplet Theorem for Random Cluster Models -- Phase Coexistence for the Kacโ{128}{148}Ising Models -- Sharp Estimates for Brownian Non-intersection Probabilities -- Tagged Particle Distributions or How to Choose a Head at Random -- Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice -- Current Fluctuations for the Totally Asymmetric Simple Exclusion Process -- Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane -- Hydrodynamic Equation for a Deposition Model -- Time Reversal of Degenerate Diffusions -- Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited -- Directed Percolation and Random Walk -- Entanglement and Rigidity in Percolation Models -- On Critical Values for Some Random Processes with Local Interaction in R2 -- The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited -- Gibbs Measures on Brownian Paths -- Geometric and Probabilistic Aspects of Boson Lattice Models -- Thermodynamical Aspects of Classical Lattice Systems
