In and out of equilibrium平衡的内外

2002-4  

Sidoravicius, Vladas  

472  

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades, specifically covering such subjects as percolation theory, random walks, interacting particle systems, and various topics related to statistical mechanics. 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 some of the most distinguished 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. Contributors: K. Alexander * J.M. Azaïs * 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. Prähofer * C. Roberto * O. Schramm * V. Sidoravicius * H. Spohn * A. Toom * B. Tóth * D. Ueltschi * W. Werner * M. Wschebor * M. Wüthrich Graduate students and researchers in probability theory and math physics will find this book a useful reference.

PrefaceRandomly Coalescing Random Walk in Dimension≥3The Single Droplet Theorem for Random Cluster ModelsPhase Coexistence for the Kac-Ising ModelsSharp Estimates for Brownian Non-intersection ProbabilitiesTagged Particle Distributions or How to Choose a Head at RandomApproach to Fixation for Zero-Temperature Stochastic Ising Modelson the Hexagonal LatticeCurrent Fluctuations for the Totally Asymmetric Simple Exclusion ProcessAsymptotic Behaviour of Semi-Infinite Geodesics for MaximalIncreasing Subsequences in the PlaneHydrodynamic Equation for a Deposition ModelTime Reversal of Degenerate DiffusionsSpectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition RevisitedDirected Percolation and Random WalkEntanglement and Rigidity in Percolation ModelsOn Critical Values for Some Random Processes withLocal Interaction in R2Tbe Distribution of the Maximum of a Gaussian Process Rice Method RevisitedGibbs Measures on Brownian PathsGeometric and Probabilistic Aspects of Boson Lattice ModelsThermodynamical Aspects of Classical Lattice Systems

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