Steady states, fluctuation-dissipation theorems and homogenization for reversible diffusions in a random environment

DOI10.1007/s00205-018-1245-1zbMath1408.35235arXiv1601.02944OpenAlexW2796101078MaRDI QIDQ1783951

Andrey L. Piatnitski, Pierre Mathieu

Publication date: 21 September 2018

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02944

zbMATH Keywords

homogenizationsteady statefluctuation-dissipation theoremparticle system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Diffusion processes (60J60) Processes in random environments (60K37) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Annealed estimates on the Green functions and uncertainty quantification
• Variance decay for functionals of the environment viewed by the particle
• Asymptotic expansion of the invariant measure for ballistic random walk in the low disorder regime
• An invariance principle for reversible Markov processes. Applications to random motions in random environments
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Dirichlet forms and symmetric Markov processes
• The Einstein relation for the displacement of a test particle in a random environment
• On ballistic diffusions in random environment
• A law of large numbers for random walks in random environment
• Elliptic partial differential equations of second order
• Quantitative results on the corrector equation in stochastic homogenization
• On mobility and Einstein relation for tracers in time-mixing random environments
• Statistical physics II. Nonequilibrium statistical mechanics.
• Einstein relation and steady states for the random conductance model
• Einstein relation for reversible diffusions in a random environment
• A simple framework to justify linear response theory
• AVERAGING OF RANDOM OPERATORS
• The method of averaging and walks in inhomogeneous environments
• Linear response, or else
• Fluctuations in Markov Processes

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