Stochastic dynamics on product manifolds: twenty five years after
UDC 519.21; 517.9 We consider an infinite system of stochastic differential equations in a compact manifold $\mathcal{M}.$ The equations are labeled by vertices of a geometric graph with unbounded vertex degrees and coupled via the nearest neighbor interaction. We prove the global existence and uniq...
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| Дата: | 2026 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8411 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513067448664064 |
|---|---|
| author | Daletskii, Alexei Daletskii, Alexei |
| author_facet | Daletskii, Alexei Daletskii, Alexei |
| author_sort | Daletskii, Alexei |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:30:56Z |
| description | UDC 519.21; 517.9
We consider an infinite system of stochastic differential equations in a compact manifold $\mathcal{M}.$ The equations are labeled by vertices of a geometric graph with unbounded vertex degrees and coupled via the nearest neighbor interaction. We prove the global existence and uniqueness of strong solutions and construct in this way the stochastic dynamics associated with Gibbs measures that describes equilibrium states of a (quenched) system of particles with positions, which form a typical realization of a Poisson or Gibbs point process in $\mathbb{R}^{d}.$ |
| doi_str_mv | 10.3842/umzh.v77i4.8411 |
| first_indexed | 2026-03-24T03:38:47Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8411 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:47Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-84112026-03-21T13:30:56Z Stochastic dynamics on product manifolds: twenty five years after Stochastic dynamics on product manifolds: twenty five years after Daletskii, Alexei Daletskii, Alexei Infinite product manifolds stochastic differential equations Gibbs measures UDC 519.21; 517.9 We consider an infinite system of stochastic differential equations in a compact manifold $\mathcal{M}.$ The equations are labeled by vertices of a geometric graph with unbounded vertex degrees and coupled via the nearest neighbor interaction. We prove the global existence and uniqueness of strong solutions and construct in this way the stochastic dynamics associated with Gibbs measures that describes equilibrium states of a (quenched) system of particles with positions, which form a typical realization of a Poisson or Gibbs point process in $\mathbb{R}^{d}.$ УДК 519.21; 517.9 Стохастична динаміка на добутках многовидів: двадцять п'ять років після Розглянуто нескінченну систему стохастичних диференціальних рівнянь на компактному многовиді~$\mathcal{M}$. Рівняння проіндексовано вершинами геометричного графа з необмеженими степенями, а взаємодію між ними реалізовано за принципом найближчих сусідів. Доведено глобальне існування та єдиність сильних розв'язків. Побудовано відповідну стохастичну динаміку, пов'язану з гіббсівськими мірами, що описують рівноважні стани (замороженої) системи частинок, просторові конфігурації яких є типовою реалізацією пуассонівського або гіббсівського точкового процесу в~$\mathbb{R}^{d}$. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8411 10.3842/umzh.v77i4.8411 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 4 (2025); 280–281 Український математичний журнал; Том 77 № 4 (2025); 280–281 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8411/10442 Copyright (c) 2025 Alexei Daletskii |
| spellingShingle | Daletskii, Alexei Daletskii, Alexei Stochastic dynamics on product manifolds: twenty five years after |
| title | Stochastic dynamics on product manifolds: twenty five years after |
| title_alt | Stochastic dynamics on product manifolds: twenty five years after |
| title_full | Stochastic dynamics on product manifolds: twenty five years after |
| title_fullStr | Stochastic dynamics on product manifolds: twenty five years after |
| title_full_unstemmed | Stochastic dynamics on product manifolds: twenty five years after |
| title_short | Stochastic dynamics on product manifolds: twenty five years after |
| title_sort | stochastic dynamics on product manifolds: twenty five years after |
| topic_facet | Infinite product manifolds stochastic differential equations Gibbs measures |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8411 |
| work_keys_str_mv | AT daletskiialexei stochasticdynamicsonproductmanifoldstwentyfiveyearsafter AT daletskiialexei stochasticdynamicsonproductmanifoldstwentyfiveyearsafter |