This volume celebrates the tenth edition of the Brazilian School of Probability (EBP), held at IMPA, Rio de Janeiro, from July 30 to August 4, 2006, jointly with the 69th Annual Meeting of the Institute of Mathematical Statistics. It was indeed an exceptional occasion for the local community working in this ?eld. The EBP, ?rst envisioned and organized in 1997, has since developed into an annual meeting with two or three advanced mini-courses and a high level conference. This volume grew up from invited or contributed articles by researchers that during the last ten yearshave been participating in the BrazilianSchool of Pro- bility. As a consequence, its content partially re?ects the topics that have pred- inated in the activities during the various editions of the School, with a strong - peal that comes from statistical mechanics and areasof concentrationthat include interacting particlesystems, percolation, random media anddisordered systems. All articles of this volume were peer-refereed.

"The intersection of probability and physics has been a rich and explosive area of growth in the past three decades, specifically covering such subjects as percolation theory, random walks in random environment, disordered systems, interacting particle systems and their many connections to statistical mechanics. The last decade was particularly fruitful for all these topics. This book reflects this development and marks also the first decade of the Brazilian School of Probability.

Poisson Approximations via Chen-Stein for Non-Markov Processes.- An Inequality for Oriented 2-D Percolation.- Is Critical 2D Percolation Universal?.- A New REM Conjecture.- The Biham-Middleton-Levine Traffic Model for a Single Junction.- Box-Crossings and Continuity Results for Self-Destructive Percolation in the Plane.- A Quenched Invariance Principle for Certain Ballistic Random Walks in i.i.d. Environments.- Homogenenous Multitype Fragmentations.- A Hierarchical Bayes Model for Combining Precipitation Measurements from Different Sources.- A Lower Bound on the Disconnection Time of a Discrete Cylinder.- On the Large Deviations Properties of the Weighted-Serve-the-Longest-Queue Policy.- Exponential Inequalities for Empirical Unbounded Context Trees.- Spatial Point Processes and the Projection Method.- An Improvement on Vajda's Inequality.- Space-Time Percolation.- Computability of Percolation Thresholds.- Chip-Firing and Rotor-Routing on Directed Graphs.- Ising Model Fog Drip: The First Two Droplets.- Convergence to Fractional Brownian Motion and to the Telecom Process: the Integral Representation Approach.- Positive Recurrence of a One-Dimensional Variant of Diffusion Limited Aggregation.- Gibbsian Description of Mean-Field Models.- What is the Difference Between a Square and a Triangle?.- Long-Range Dependence in Mean and Volatility: Models, Estimation and Forecasting.- Percolation in the Sherrington-Kirkpatrick Spin Glass.- A Note on the Diffusivity of Finite-Range Asymmetric Exclusion Processes on ?.- On the Role of Spatial Aggregation in the Extinction of a Species.- Systems of Random Equations. A Review of Some Recent Results.