Ebook: Probability and Phase Transition

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability.
The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

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This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability.
The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

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This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability.
The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

Content:
Front Matter....Pages i-xvi
Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model....Pages 1-16
Droplet Condensation in the Ising Model: Moderate Deviations Point of View....Pages 17-34
Shocks in one-Dimensional Processes with Drift....Pages 35-48
Self-Organization of Random Cellular Automata: Four Snapshots....Pages 49-67
Percolative Problems....Pages 69-86
Mean-Field Behaviour and the Lace Expansion....Pages 87-122
Long Time Tails in Physics and Mathematics....Pages 123-137
Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment....Pages 139-152
Geometric Representation of Lattice Models and Large Volume Asymptotics....Pages 153-176
Diffusion in Random and Non-Linear PDE’s....Pages 177-189
Random Walks, Harmonic Measure, and Laplacian Growth Models....Pages 191-208
Survival and Coexistence in Interacting Particle Systems....Pages 209-226
Constructive Methods in Markov Chain Theory....Pages 227-236
A Stochastic Geometric Approach to Quantum Spin Systems....Pages 237-246
Disordered Ising Systems and Random Cluster Representations....Pages 247-260
Planar First-Passage Percolation Times are not Tight....Pages 261-264
Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models....Pages 265-301
Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas....Pages 303-322

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This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability.
The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

Content:
Front Matter....Pages i-xvi
Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model....Pages 1-16
Droplet Condensation in the Ising Model: Moderate Deviations Point of View....Pages 17-34
Shocks in one-Dimensional Processes with Drift....Pages 35-48
Self-Organization of Random Cellular Automata: Four Snapshots....Pages 49-67
Percolative Problems....Pages 69-86
Mean-Field Behaviour and the Lace Expansion....Pages 87-122
Long Time Tails in Physics and Mathematics....Pages 123-137
Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment....Pages 139-152
Geometric Representation of Lattice Models and Large Volume Asymptotics....Pages 153-176
Diffusion in Random and Non-Linear PDE’s....Pages 177-189
Random Walks, Harmonic Measure, and Laplacian Growth Models....Pages 191-208
Survival and Coexistence in Interacting Particle Systems....Pages 209-226
Constructive Methods in Markov Chain Theory....Pages 227-236
A Stochastic Geometric Approach to Quantum Spin Systems....Pages 237-246
Disordered Ising Systems and Random Cluster Representations....Pages 247-260
Planar First-Passage Percolation Times are not Tight....Pages 261-264
Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models....Pages 265-301
Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas....Pages 303-322
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