Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration inequalities for the hydrodynamic limit of a two-species
  stochastic particle system   We study a stochastic particle system which is motivated from grain boundary
coarsening in two-dimensional networks. Each particles lives on the positive
real line and is labeled as belonging to either Species 1 or Species 2. Species
1 particles drift at unit speed toward the origin, while Species 2 particles do
not move. When a particle in Species 1 hits the origin, it is removed, and a
randomly selected particle mutates from Species 2 to Species 1. The process
described is an example of a high-dimensional piecewise deterministic Markov
process (PDMP), in which deterministic flow is punctuated with stochastic
jumps. Our main result is a proof of exponential concentration inequalities of
the Kolmogorov-Smirnoff distance between empirical measures of the particle
system and solutions of limiting nonlinear kinetic equations. Our method of
proof involves a time and space discretization of the kinetic equations, which
we compare with the particle system to derive recurrence inequalities for
comparing total numbers in small intervals. To show these recurrences occur
with high probability, we appeal to a state dependent Hoeffding type inequality
at each time increment.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph