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Dynamical clusters of infinite particle dynamics

Authors
  • Malyshev, V. A.
Type
Published Article
Publication Date
Dec 16, 2011
Submission Date
Dec 16, 2011
Identifiers
arXiv ID: 1112.3796
Source
arXiv
License
Yellow
External links

Abstract

For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff for some $t\in[0,\tau]$ the distance between particles $i,j$ is not greater than some constant. We undertake a detailed study of this graph for infinite particle dynamics and prove exponential estimates for its finite connected components. This solves continuous percolation problem for a complicated geometrical objects - the tubes around particle trajectories.

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