Abstract
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
nearest neighbour interaction. We prove the global existence and
uniqueness of strong solutions and construct in this way stochastic dynamics associated with Gibbs measures describing equilibrium states of a (quenched) system of particles with positions forming a typical realization of a Poisson or Gibbs point process in Rd.
in a compact manifold M. The equations are labeled by vertices of
a geometric graph with unbounded vertex degrees and coupled via
nearest neighbour interaction. We prove the global existence and
uniqueness of strong solutions and construct in this way stochastic dynamics associated with Gibbs measures describing equilibrium states of a (quenched) system of particles with positions forming a typical realization of a Poisson or Gibbs point process in Rd.
| Original language | English |
|---|---|
| Number of pages | 21 |
| Journal | Ukrainian Mathematical Journal |
| Publication status | Accepted/In press - 12 Sept 2024 |
Bibliographical note
This is an author-produced version of the published paper. Uploaded in accordance with the University’s Research Publications and Open Access policy.Keywords
- Infinite product manifold
- Gibbs measure
- stochastic equation