Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

DOI10.1088/0951-7715/28/11/4117zbMath1357.37010arXiv1412.0848OpenAlexW2963968107MaRDI QIDQ3458804

Manuel Stadlbauer, Artur Oscar Lopes, Benoît R. Kloeckner

Publication date: 23 December 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0848

zbMATH Keywords

spectral gapRuelle operatorWasserstein spaceoptimal couplingcoupling techniques

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Optimality conditions for problems involving randomness (49K45)

Related Items (10)

A formula for the entropy of the convolution of Gibbs probabilities on the circle ⋮ Entropy, pressure, ground states and calibrated sub-actions for linear dynamics ⋮ A Ruelle-Perron-Frobenius theorem for expanding circle maps with an indifferent fixed point ⋮ Quenched and annealed equilibrium states for random Ruelle expanding maps and applications ⋮ A linear response for dynamical systems with additive noise ⋮ Empirical measures: regularity is a counter-curse to dimensionality ⋮ Ergodic and thermodynamic games ⋮ An optimal transportation approach to the decay of correlations for non-uniformly expanding maps ⋮ Nonequilibrium in thermodynamic formalism: the second law, gases and information geometry ⋮ Invariant probabilities for discrete time linear dynamics via thermodynamic formalism ^*

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• On the Existence of Conformal Measures
• Stability of the maximal measure for piecewise monotonic interval maps
• Linear response formula for piecewise expanding unimodal maps
• Optimal Transport
• Differentiability of thermodynamical quantities in non uniformly expanding dynamics

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