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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
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spelling 2025-03-11T13:58:46.8763446 v2 68991 2025-02-28 Stochastic dynamics of particle systems on unbounded degree graphs 78921ede79d2c1e329edc5a24beb7206 Georgy Chargaziya Georgy Chargaziya true false 2025-02-28 MACS 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. Journal Article Journal of Mathematical Physics 66 2 023508 AIP Publishing 0022-2488 1089-7658 18 2 2025 2025-02-18 10.1063/5.0169112 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee 2025-03-11T13:58:46.8763446 2025-02-28T11:34:02.5175805 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Georgy Chargaziya 1 Alexei Daletskii 0000-0003-3185-9806 2 68991__33709__46f8ba058ac9478fbfccf87d13d5adc7.pdf 68991.VOR.pdf 2025-02-28T11:45:21.2219743 Output 4456462 application/pdf Version of Record true © 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license. true eng https://creativecommons.org/licenses/by/4.0/
title Stochastic dynamics of particle systems on unbounded degree graphs
spellingShingle Stochastic dynamics of particle systems on unbounded degree graphs
Georgy Chargaziya
title_short Stochastic dynamics of particle systems on unbounded degree graphs
title_full Stochastic dynamics of particle systems on unbounded degree graphs
title_fullStr Stochastic dynamics of particle systems on unbounded degree graphs
title_full_unstemmed Stochastic dynamics of particle systems on unbounded degree graphs
title_sort Stochastic dynamics of particle systems on unbounded degree graphs
author_id_str_mv 78921ede79d2c1e329edc5a24beb7206
author_id_fullname_str_mv 78921ede79d2c1e329edc5a24beb7206_***_Georgy Chargaziya
author Georgy Chargaziya
author2 Georgy Chargaziya
Alexei Daletskii
format Journal article
container_title Journal of Mathematical Physics
container_volume 66
container_issue 2
container_start_page 023508
publishDate 2025
institution Swansea University
issn 0022-2488
1089-7658
doi_str_mv 10.1063/5.0169112
publisher AIP Publishing
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2025-02-18T08:40:48Z
_version_ 1830359503833399296
score 11.059615

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