Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative Rates of Convergence to Equilibrium for the Degenerate
  Linear Boltzmann equation on the Torus   We study the linear relaxation Boltzmann equation on the torus with a
spatially varying jump rate which can be zero on large sections of the domain.
In \cite{BS13} Bernard and Salvarani showed that this equation converges
exponentially fast to equilibrium if and only if the jump rate satisfies the
geometric control condition of Bardos, Lebeau and Rauch \cite{BLR91}. In
\cite{HL15} Han-Kwan and L\'{e}autaud showed a more general result for linear
Boltzmann equations under the action of potentials in different geometric
contexts, including the case of unbounded velocities. In this paper we obtain
quantitative rates of convergence to equilibrium when the geometric control
condition is satisfied, using a probabilistic approach based on Doeblin's
theorem from Markov chains.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con