Overview

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.

Full Product Details

Author:   G.R. Grimmett
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1994
Volume:   420
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.522kg
ISBN:  

9789048143702

ISBN 10:   9048143705
Pages:   322
Publication Date:   15 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model.- Droplet Condensation in the Ising Model: Moderate Deviations Point of View.- Shocks in one-Dimensional Processes with Drift.- Self-Organization of Random Cellular Automata: Four Snapshots.- Percolative Problems.- Mean-Field Behaviour and the Lace Expansion.- Long Time Tails in Physics and Mathematics.- Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment.- Geometric Representation of Lattice Models and Large Volume Asymptotics.- Diffusion in Random and Non-Linear PDE’s.- Random Walks, Harmonic Measure, and Laplacian Growth Models.- Survival and Coexistence in Interacting Particle Systems.- Constructive Methods in Markov Chain Theory.- A Stochastic Geometric Approach to Quantum Spin Systems.- Disordered Ising Systems and Random Cluster Representations.- Planar First-Passage Percolation Times are not Tight.- Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models.- Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas.

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