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<p>We consider an infinite system of stochastic differential equations in a compact manifold ℳ<i>.</i> 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 ℝ<sup><i>d</i></sup><i>.</i></p>

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Stochastic Dynamics on Product Manifolds: Twenty Five Years After

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Alexei Daletskii

摘要

We consider an infinite system of stochastic differential equations in a compact manifold 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 ℝd.