Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e inequality and the Lp convergence of semi-groups   We prove that for symmetric Markov processes of diffusion type admitting a
"carr\'e du champ", the Poincar\'e inequality is equivalent to the exponential
convergence of the associated semi-group in one (resp. all) $\L^p(\mu)$ spaces
for $p\in (1,+\infty)$. Part of this result extends to the stationary non
necessarily symmetric situation.

0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci