In and Out of Equilibrium

1. Front Matter

   Pages i-vii

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2. Randomly Coalescing Random Walk in Dimension ≥3

   • J. van den Berg, Harry Kesten

   Pages 1-45

3. The Single Droplet Theorem for Random Cluster Models

   • Kenneth Alexander

   Pages 47-73

4. Phase Coexistence for the Kac-Ising Models

   • Thierry Bodineau

   Pages 75-111

5. Sharp Estimates for Brownian Non-intersection Probabilities

   • Gregory F. Lawler, Oded Schramm, Wendelin Werner

   Pages 113-131

6. Tagged Particle Distributions or How to Choose a Head at Random

   • Thomas M. Liggett

   Pages 133-162

7. Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice

   • Federico Camia, Charles M. Newman, Vladas Sidoravicius

   Pages 163-183

8. Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

   • Michael Prähofer, Herbert Spohn

   Pages 185-204

9. Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane

   • Mario V. Wüthrich

   Pages 205-226

10. Hydrodynamic Equation for a Deposition Model

    • Bálint Tóth, Wendelin Werner

    Pages 227-248

11. Time Reversal of Degenerate Diffusions

    • Jeremy Quastel

    Pages 249-257

12. Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited

    • Nicoletta Cancrini, Fabio Martinelli, Cyril Roberto

    Pages 259-271

13. Directed Percolation and Random Walk

    • Geoffrey Grimmett, Philipp Hiemer

    Pages 273-297

14. Entanglement and Rigidity in Percolation Models

    • Alexander E. Holroyd

    Pages 299-307

15. On Critical Values for Some Random Processes with Local Interaction in R2

    • André Toom

    Pages 309-319

16. The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited

    • Jean-Marc Azaïs, Mario Wschebor

    Pages 321-348

17. Gibbs Measures on Brownian Paths

    • József Lőrinczi

    Pages 349-362

18. Geometric and Probabilistic Aspects of Boson Lattice Models

    • Daniel Ueltschi

    Pages 363-391

19. Thermodynamical Aspects of Classical Lattice Systems

    • Charles-Edouard Pfister

    Pages 393-472

For more than two decades percolation theory, random walks, interacting parti­ cle systems and topics related to statistical mechanics have experienced inten­ sive growth. In the last several years, especially remarkable progress has been made in a number of directions, such as: Wulff constructions above two dimen­ sions for percolation, Potts and Ising models, classification of random walks in random environments, better understanding of fluctuations in two dimen­ 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 crit­ 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.

• Maxima
• Probability theory
• Theoretical physics
• Variance
• dynamics
• math physics
• mechanics
• statistical mechanics

• IMPA-Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

  Vladas Sidoravicius

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