A consistency estimate for Kac's model of elastic collisions in a dilute gas

DOI10.1214/15-AAP1111zbMath1339.60140arXiv1405.2742OpenAlexW2257593935MaRDI QIDQ292918

James R. Norris

Publication date: 9 June 2016

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.2742

zbMATH Keywords

law of large numbersBoltzmann equationWasserstein distancedilute gaselastic collisionsKac model

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Strong limit theorems (60F15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

Related Items

Kac's process with hard potentials and a moderate angular singularity ⋮ Large deviations of Kac's conservative particle system and energy nonconserving solutions to the Boltzmann equation: a counterexample to the predicted rate function ⋮ Variational methods for evolution. Abstracts from the workshop held November 12--18, 2017 ⋮ Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials ⋮ Pathwise convergence of the hard spheres Kac process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules
• Quantitative propagation of chaos for generalized Kac particle systems
• Kac's program in kinetic theory
• Constructive quantization: approximation by empirical measures
• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• On the rate of convergence in Wasserstein distance of the empirical measure
• On measure solutions of the Boltzmann equation. I: Moment production and stability estimates
• Differential equation approximations for Markov chains
• On the spatially homogeneous Boltzmann equation
• Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation
• A Note on Maximal Inequality for Stochastic Convolutions
• [https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
• A note on stochastic convolution
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules