2005/03/02 by Yu. G. Kondratiev, Eugene Lytvynov, E. Lytvynov +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60J75 #60J80 #60K35 #82C21 #82C22 #FOS: Mathematics #FOS: Physical sciences #Hemoglobin structure and function #Lipid Membrane Structure and Behavior #Mathematical Physics (math-ph) #Probability (math.PR) #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #math.PR #msc:60J75 #msc:60J80 #msc:60K35 #msc:82C21 #msc:82C22
paper · pdf · doi:10.48550/arxiv.math/0503042
openalex publication_date 2005/03/02 · arxiv created 2007/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold X. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over X. We establish conditions on the \it a priori explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).