Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equidistribution of mass for random processes on finite-volume spaces   Let $G$ be a real Lie group, $\Lambda\subseteq G$ a lattice, and
$X=G/\Lambda$. We fix a probability measure $\mu$ on $G$ and consider the left
random walk induced on $X$. It is assumed that $\mu$ is aperiodic, has a finite
first moment, spans a semisimple algebraic group without compact factors, and
has two non mutually singular convolution powers. We show that for every
starting point $x\in X$, the $n$-th step distribution $\mu^n*\delta_{x}$ of the
walk weak-$\ast$ converges toward some homogeneous probability measure on $X$.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph