Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-collision and collision properties of Dyson's model in infinite
  dimension and other stochastic dynamics whose equilibrium states are
  determinantal random point fields   Dyson's model on interacting Brownian particles is a stochastic dynamics
consisting of an infinite amount of particles moving in $ \R $ with a
logarithmic pair interaction potential. For this model we will prove that each
pair of particles never collide.
  The equilibrium state of this dynamics is a determinantal random point field
with the sine kernel. We prove for stochastic dynamics given by Dirichlet forms
with determinantal random point fields as equilibrium states the particles
never collide if the kernel of determining random point fields are locally
Lipschitz continuous, and give examples of collision when H\"older continuous.
  In addition we construct infinite volume dynamics (a kind of infinite
dimensional diffusions) whose equilibrium states are determinantal random point
fields. The last result is partial in the sense that we simply construct a
diffusion associated with the {\em maximal closable part} of {\em canonical}
pre Dirichlet forms for given determinantal random point fields as equilibrium
states. To prove the closability of canonical pre Dirichlet forms for given
determinantal random point fields is still an open problem. We prove these
dynamics are the strong resolvent limit of finite volume dynamics.

24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci