Riassunto
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.
Contenuti
Van den Berg, J., Kesten, H.: Randomly Coalescing Random Walk in Dimension = 3 * Alexander, K.: The Single Droplet Theorem for Random Cluster Models * Bodineau, T.: Phase Coexistence for the Kac Ising Models * Lawler, G.F., Schramm, O., Werner, W.: Sharp Estimates for Brownian Non-intersection Probabilities * Liggett, T.M.: Tagged Particle Distributions or How to Choose a Head at Random * Camia, F., Newman, C.M., Sidoravicius, V.: Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice * Prahofer, M., Spohn, H.: Current Fluctuations for the Totally Asymmetric Simple Exclusion Process * Wuthrich, M.V.: Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane * Toth, B., Werner, W.: Hydrodynamic Equation for a Deposition Model * Quastel, J.: Time Reversal of Degenerate Diffusions * Cancrini, N., Martinelli, F., Roberto, C.: Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited * Grimmett, G., Hiemer, P.: Directed Percolation and Random Walk * Holroyd, A.E.: Entanglement and Rigidity In Percolation Models * Toom, A.: On Critical Values for Some Random Processes with Local Interaction in R^2 * Azais, J.-M., Wschebor, M.: The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited * Lorinczi, J.: Gibbs Measures on Brownian Paths * Ueltschi, D.: Geometric and Probabilistic Aspects of Boson Lattice Models * Pfister, C.-E.: Thermodynamical Aspects of Classical Lattice Systems
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