Ebook: In and Out of Equilibrium: Probability with a Physics Flavor
- Tags: Statistical Theory and Methods, Applications of Mathematics, Mathematical Methods in Physics
- Series: Progress in Probability 51
- Year: 2002
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-vii
Randomly Coalescing Random Walk in Dimension ?3....Pages 1-45
The Single Droplet Theorem for Random Cluster Models....Pages 47-73
Phase Coexistence for the Kac-Ising Models....Pages 75-111
Sharp Estimates for Brownian Non-intersection Probabilities....Pages 113-131
Tagged Particle Distributions or How to Choose a Head at Random....Pages 133-162
Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice....Pages 163-183
Current Fluctuations for the Totally Asymmetric Simple Exclusion Process....Pages 185-204
Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane....Pages 205-226
Hydrodynamic Equation for a Deposition Model....Pages 227-248
Time Reversal of Degenerate Diffusions....Pages 249-257
Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited....Pages 259-271
Directed Percolation and Random Walk....Pages 273-297
Entanglement and Rigidity in Percolation Models....Pages 299-307
On Critical Values for Some Random Processes with Local Interaction in R2 ....Pages 309-319
The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited....Pages 321-348
Gibbs Measures on Brownian Paths....Pages 349-362
Geometric and Probabilistic Aspects of Boson Lattice Models....Pages 363-391
Thermodynamical Aspects of Classical Lattice Systems....Pages 393-472
Content:
Front Matter....Pages i-vii
Randomly Coalescing Random Walk in Dimension ?3....Pages 1-45
The Single Droplet Theorem for Random Cluster Models....Pages 47-73
Phase Coexistence for the Kac-Ising Models....Pages 75-111
Sharp Estimates for Brownian Non-intersection Probabilities....Pages 113-131
Tagged Particle Distributions or How to Choose a Head at Random....Pages 133-162
Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice....Pages 163-183
Current Fluctuations for the Totally Asymmetric Simple Exclusion Process....Pages 185-204
Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane....Pages 205-226
Hydrodynamic Equation for a Deposition Model....Pages 227-248
Time Reversal of Degenerate Diffusions....Pages 249-257
Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited....Pages 259-271
Directed Percolation and Random Walk....Pages 273-297
Entanglement and Rigidity in Percolation Models....Pages 299-307
On Critical Values for Some Random Processes with Local Interaction in R2 ....Pages 309-319
The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited....Pages 321-348
Gibbs Measures on Brownian Paths....Pages 349-362
Geometric and Probabilistic Aspects of Boson Lattice Models....Pages 363-391
Thermodynamical Aspects of Classical Lattice Systems....Pages 393-472
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