An introduction to metastability through random walks
type: Item
instance of: scholarly article
title: An introduction to metastability through random walks
zbMATH Open document ID: 1200.82042
DOI: 10.1214/09-BJPS035
author: E. Olivieri
author: E. Scoppola
published in: Brazilian Journal of Probability and Statistics
publication date: 2010-08-09T00:00:00Z
review text: The paper is a guide for beginners into the metastability problem which is a dynamical phenomenon taking place in the vicinity of a first order phase transition in a lattice spin system. The physical motivation is that of a ferromagnetic behavior. Its formal implementation is given in terms of the Ising model, with emphasis on Glauber and Kawasaki modifications of the original model. The principal aim of the authors is to describe the evolution of a metastable state and its decay to the stable equilibrium through the nucleation to the stable phase. Major mathematical techniques come from the Wentzell-Freidlin theory of small random perturbations of dynamical systems and also involve analytical methods to control the convergence to equilibrium of a random process, by means of the spectral properties of its generator.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82C20
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 82C41
Mathematics Subject Classification ID: 82C80
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 5764987
zbMATH Keywords: random walks
zbMATH Keywords: Markov chains
zbMATH Keywords: phase transitions
zbMATH Keywords: metastability
zbMATH Keywords: Ising models
zbMATH Keywords: Glauber dynamics
zbMATH Keywords: Kawasaki dynamics
zbMATH Keywords: Monte Carlo method
zbMATH Keywords: small random perturbations
zbMATH Keywords: large deviations
zbMATH Keywords: Wentzell-Freidlin limit theorems
MaRDI profile type: Publication
cites work: Q5395377
cites work: Metastability of the three dimensional Ising model on a torus at very low temperatures
cites work: Sharp asymptotics for Kawasaki dynamics on a finite box with open boundary
cites work: Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymp\-totics.
cites work: Metastability in stochastic dynamics of disordered mean-field models
cites work: The exit path of a Markov chain with rare transitions
cites work: Metastable behavior of stochastic dynamics: A pathwise approach
cites work: Metastability for a stochastic dynamics with a parallel heat bath updating rule
cites work: Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition.
cites work: A nucleation-and-growth model
cites work: Metropolis dynamics relaxation via nucleation and growth
cites work: Large deviations
cites work: Metastability and nucleation for conservative dynamics
cites work: Q3706275
cites work: Q3672830
cites work: Q4259433
cites work: Collision probability for random trajectories in two dimensions
cites work: Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics
cites work: Q5290628
cites work: Finite Markov Chains and Algorithmic Applications
cites work: Q4239083
cites work: The Metastable Behavior of Infrequently Observed, Weakly Random, One-Dimensional Diffusion Processes
cites work: Droplet dynamics for asymmetric Ising model
cites work: Shapes of growing droplets -- a model of escape from a metastable phase
cites work: Rigorous Treatment of the Van Der Waals-Maxwell Theory of the Liquid-Vapor Transition
cites work: On the essential features of metastability: Tunnelling time and critical configurations
cites work: Q4342612
cites work: Anisotropy effects in nucleation for conservative dynamics
cites work: On the Ising model with strongly anisotropic external field
cites work: Critical droplets and metastability for a Glauber dynamics at very low temperatures
cites work: Behavior of droplets for a class of Glauber dynamics at very low temperature
cites work: Markov chains with exponentially small transition probabilities: first exit problem from a general domain. I: The reversible case.
cites work: Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II: The general case.
cites work: Q4208241
cites work: Large Deviations and Metastability
cites work: The pattern of escape from metastability of a stochastic Ising model
cites work: Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region
cites work: Q4848564
cites work: Wulff droplets and the metastable relaxation of kinetic Ising models
cites work: Renormalization group for Markov chains and application to metastability
cites work: Q4848565
cites work: Q3968213
description: scientific article; zbMATH DE number 5764987