Stochastic dynamics of particle systems on unbounded degree graphs
Year: 2025
Type: article
Abstract: We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each particle is characterized by its position x∈Rd and internal parameter (spin) σx∈R. While the positions of particles form a fixed (“quenched”) locally-finite set (configuration) γ⊂Rd, the spins σx and σy interact via a pair potential whenever x−y<ρ, where ρ > 0 is a fixed interaction radius. The number nx of particles interacting with a particle in position x is finite but unbounded in x. The growth of nx as |x| → ∞ creates a major technical problem for solving our SDE system. To overcome this problem, we use a finite volume approximation combined with a version of the Ovsjannikov method, and prove the existence and uniqueness of the solution in a scale of Banach spaces of weighted sequences. As an application example, we construct stochastic dynamics associated with Gibbs states of our particle system.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0169112
Authors: Georgy Chargaziya, Alexei Daletskii
Institutions: Swansea University, University of York
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4407699960