Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical clusters of infinite particle dynamics   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.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg