Metastability and low lying spectra in reversible Markov chains

From MaRDI portal
Publication:1849267

DOI10.1007/s002200200609zbMath1010.60088arXivmath/0007160OpenAlexW2090987881MaRDI QIDQ1849267

Michael Eckhoff, Anton Bovier, Véronique Gayrard, Markus Klein

Publication date: 1 December 2002

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0007160




Related Items

Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environmentHitting time asymptotics for hard-core interactions on gridsCritical droplets and sharp asymptotics for Kawasaki dynamics with weakly anisotropic interactionsA graph-algorithmic approach for the study of metastability in Markov chainsMetastability of the nonlinear wave equation: insights from transition state theoryCritical configurations and tube of typical trajectories for the Potts and Ising models with zero external fieldMetastability for the degenerate Potts model with negative external magnetic field under Glauber dynamicsMetastable states, quasi-stationary distributions and soft measuresNon-reversible metastable diffusions with Gibbs invariant measure. I: Eyring-Kramers formulaMetastability for Glauber dynamics on the complete graph with coupling disorderNonlinear Markov processes in big networksOn times to quasi-stationarity for birth and death processesGlauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastabilityFinding Dominant Structures of Nonreversible Markov ProcessesMetastability of the two-dimensional Blume-Capel model with zero chemical potential and small magnetic fieldAbrupt convergence and escape behavior for birth and death chainsMulti-scale metastable dynamics and the asymptotic stationary distribution of perturbed Markov chainsSum of Exit Times in Series of Metastable States in Probabilistic Cellular AutomataBasic Ideas to Approach Metastability in Probabilistic Cellular AutomataRandom walks and polymers in the presence of quenched disorderGround states for mean field models with a transverse componentOn soft capacities, quasi-stationary distributions and the pathwise approach to metastabilityThe tunneling effect for a class of difference operatorsMetastability for the Ising model on the hypercubeMetastable distributions of Markov chains with rare transitionsOn the diffusion geometry of graph Laplacians and applicationsAging in metropolis dynamics of the REM: a proofSpectral analysis for a discrete metastable system driven by Lévy flightsA Note on Metastable Behaviour in the Zero-Range ProcessNon-reversible metastable diffusions with Gibbs invariant measure. II: Markov chain convergenceOvercoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learningGeometric characterization of the Eyring-Kramers formulaIsing model on clustered networks: a model for opinion dynamicsCosh gradient systems and tiltingKawasaki dynamics with two types of particles: critical dropletsSpectral analysis of discrete metastable diffusionsSharp asymptotics for stochastic dynamics with parallel updating ruleTunneling and metastability of continuous time Markov chains. II: The nonreversible caseMetastability of the three-state Potts model with general interactionsLarge deviations for Lévy diffusions in the small noise regimeRelaxation height in energy landscapes: an application to multiple metastable statesHitting time of large subsets of the hypercubeTunneling for a class of difference operatorsTunneling and metastability of continuous time Markov chainsPhase transitions and metastability in Markovian and molecular systemsCut-off and exit from metastability: Two sides of the same coinComputing the asymptotic spectrum for networks representing energy landscapes using the minimum spanning treePointwise estimates and exponential laws in metastable systems via coupling methodsMetastability for reversible probabilistic cellular automata with self-interactionThe Eyring-Kramers law for Markovian jump processes with symmetriesSpectral analysis of Sinai's walk for small eigenvaluesMetastability of the Ising model on random regular graphs at zero temperatureThe Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumpsMetastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributionsMetastability of hard-core dynamics on bipartite graphsMetastability in a condensing zero-range process in the thermodynamic limitTunneling for a class of difference operators: complete asymptoticsHitting, mixing and tunneling asymptotics of Metropolis-Hastings reversiblizations in the low-temperature regimeMetastability of logit dynamics for coordination gamesHomogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperaturesA martingale approach to metastabilityMetastability under stochastic dynamicsMetastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit timesAgmon‐type estimates for a class of jump processesTunneling of the Kawasaki dynamics at low temperatures in two dimensionsSharp asymptotics of metastable transition times for one dimensional SPDEsTunneling behavior of Ising and Potts models in the low-temperature regimeMetastability in reversible diffusion processes. II: Precise asymptotics for small eigenvaluesMetastability of reversible finite state Markov processesSharp asymptotics for Kawasaki dynamics on a finite box with open boundaryPrecise asymptotics of small eigenvalues of reversible diffusions in the metastable regimeOptimal control of molecular dynamics using Markov state modelsMetastability in a continuous mean-field model at low temperature and strong interactionLandscapes of non-gradient dynamics without detailed balance: Stable limit cycles and multiple attractorsMetastability for a non-reversible dynamics: the evolution of the condensate in totally asymmetric zero range processesAsymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scalesBistable stochastic biochemical networks: large chemical networks and systems with many moleculesMetastability for the dilute Curie-Weiss model with Glauber dynamicsFlows in complex networks: theory, algorithms, and application to lennard-Jones cluster rearrangementEffect of energy degeneracy on the transition time for a series of metastable states. Application to probabilistic cellular automataPoincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalitiesMetastability of reversible random walks in potential fieldsAgmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operatorsThe first passage problem for stable linear delay equations perturbed by power law Lévy noiseDetecting localized eigenstates of linear operatorsMetastability in Markov processesMetastability in a lattice gas with strong anisotropic interactions under Kawasaki dynamicsHarmonic approximation of difference operatorsMetastability of Ising and Potts models without external fields in large volumes at low temperaturesSpectral characterization of aging: the REM-like trap modelTransient dynamics of absorbed singular diffusionsUnnamed ItemMetastability for Kawasaki dynamics on the hexagonal latticeCritical droplets and sharp asymptotics for Kawasaki dynamics with strongly anisotropic interactionsEnergy landscape and metastability of Curie-Weiss-Potts model