Exponential decay of Rényi divergence under Fokker-Planck equations
arXiv:1805.06554 · doi:10.1007/s10955-019-02339-8
Abstract
We prove the exponential convergence to the equilibrium, quantified by Rényi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential decay result on the relative entropy for the same equation.
arXiv commentExponential convergence rate in Theorem 1.2 has been improved and a simpler proof is provided
References in corpus (16)
- Rényi Divergence and Kullback-Leibler Divergence
- On quantum Renyi entropies: a new generalization and some properties
- The second laws of quantum thermodynamics
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- A step beyond Tsallis and Renyi entropies
- Monotonicity of a relative Rényi entropy
- A new class of transport distances
- alpha-z-relative Renyi entropies
- On Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities
- On Rényi and Tsallis entropies and divergences for exponential families
- A closed-form expression for the Sharma-Mittal entropy of exponential families
- Interpretations of Renyi Entropies And Divergences
- Inequalities for quantum divergences and the Audenaert-Datta conjecture
- Sandwiched Rényi Convergence for Quantum Evolutions
- Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
- Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance
Cited by in corpus (8)
- Exponential ergodicity of mirror-Langevin diffusions
- Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry
- HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation
- Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance
- Complexity of zigzag sampling algorithm for strongly log-concave distributions
- SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
- Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergence
- Hessian transport gradient flows