Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^{2}$-spectral gaps, weak-reversible and very weak-reversible Markov
  chains   The theory of $L^2$-spectral gaps for reversible Markov chains has been
studied by many authors. In this paper we consider positive recurrent general
state space Markov chains with stationary transition probabilities. Replacing
the assumption of reversibility by a less strong one, we still obtain a simple
necessary and sufficient condition for the spectral gap property of the
associated Markov operator in terms of isoperimetric constant. Moreover, we
define a new sequence of isoperimetric constants which provides a necessary and
sufficient condition for the existence of a spectral gap in a very general
setting. Finally, these results are used to obtain simple sufficient conditions
for the existence of a spectral gap in terms of the first and second order
transition probabilities.

17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph