Probability and Phase Transition

1. Auflage. Softcover version of original hardcover Auflage 1994
ISBN: 978-90-481-4370-2
Verlag: Springer Netherlands

Buch, Englisch, Band 420, 322 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 517 g

Reihe: Nato Science Series C:

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.

Zielgruppe

Research

Autoren/Hrsg.

Grimmett, G. R.

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Thermodynamik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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.