Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions

DOI10.1007/s00220-023-04659-zarXiv2112.06304MaRDI QIDQ6160258

Rishabh S. Gvalani, Matias G. Delgadino, Scott A. Smith, Grigorios A. Pavliotis

Publication date: 23 June 2023

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

Full work available at URL: https://arxiv.org/abs/2112.06304

Mathematics Subject Classification ID

Dynamical aspects of statistical mechanics (37A60) Statistical mechanics, structure of matter (82-XX)

Related Items (3)

Sharp uniform-in-time propagation of chaos ⋮ Online parameter estimation for the McKean-Vlasov stochastic differential equation ⋮ Poisson Equation on Wasserstein Space and Diffusion Approximations for Multiscale McKean–Vlasov Equation

Cites Work

• Unnamed Item
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• Reflection couplings and contraction rates for diffusions
• \{Euclidean, metric, and Wasserstein\} gradient flows: an overview
• Gibbs measures and phase transitions.
• Reflection coupling and Wasserstein contractivity without convexity
• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
• A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
• A new criterion for the logarithmic Sobolev inequality and two applications
• Dynamical aspects of mean field plane rotators and the Kuramoto model
• The McKean-Vlasov equation in finite volume
• A general two-scale criteria for logarithmic Sobolev inequalities
• Finite exchangeable sequences
• Central limit theorem for a simple diffusion model of interacting particles
• A convexity principle for interacting gases
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• A very simple proof of the LSI for high temperature spin systems
• Logarithmic Sobolev inequalities for some nonlinear PDE's.
• Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Concentration of measure and isoperimetric inequalities in product spaces
• A Hilbertian approach for fluctuations on the McKean-Vlasov model
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Dynamical aspects of the generalized Schrödinger problem via Otto calculus -- a heuristic point of view
• Metastability in a continuous mean-field model at low temperature and strong interaction
• On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions
• Quantitative approximate independence for continuous mean field Gibbs measures
• An invariance principle for gradient flows in the space of probability measures
• A \(\lambda\)-convexity based proof for the propagation of chaos for weakly interacting stochastic particles
• The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
• Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures
• Spectral gap in mean-field \({\mathcal{O}}(n)\)-model
• Mean field limit for Coulomb-type flows
• Scaling limits for interacting diffusions
• An entropic interpolation proof of the HWI inequality
• Around the entropic talagrand inequality
• Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus
• On mean-field limits and quantitative estimates with a large class of singular kernels: application to the Patlak-Keller-Segel model
• Ricci curvature for metric-measure spaces via optimal transport
• Convexity and regularity properties for entropic interpolations
• On Kac's chaos and related problems
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Symmetric Measures on Cartesian Products
• Central limit theorem for a system of Markovian particles with mean field interactions
• Analysis and Geometry of Markov Diffusion Operators
• An elementary approach to uniform in time propagation of chaos
• Stochastic Equations in Infinite Dimensions
• Stochastic Processes and Applications
• PHASE TRANSITION FROM THE VIEWPOINT OF RELAXATION PHENOMENA
• Optimal Transport
• A bifurcation theorem for potential operators
• Global-in-time mean-field convergence for singular Riesz-type diffusive flows

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