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Stochastic dynamics of particle systems on unbounded degree graphs

Georgy Chargaziya, Alexei Daletskii Orcid Logo

Journal of Mathematical Physics, Volume: 66, Issue: 2, Start page: 023508

Swansea University Author: Georgy Chargaziya

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DOI (Published version): 10.1063/5.0169112

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 ∈ Rdand internal parameter (spin) σx ∈ R. While the positions of particles form a fixed (“quenched”) local...

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Published in: Journal of Mathematical Physics
ISSN: 0022-2488 1089-7658
Published: AIP Publishing 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa68991
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 ∈ Rdand 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.
College: Faculty of Science and Engineering
Issue: 2
Start Page: 023508

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