Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the rate of convergence in the central limit theorem for hierarchical
  Laplacian   Let $(X,d)$ be a proper ultrametric space. Given a measure $m$ on $X$ and a
function $C(B)$ defined on the set of all non-singleton balls $B$ we consider
the hierarchical Laplacian $L=L_{C}$. Choosing a sequence $\{\varepsilon (B)\}$
of i.i.d. random variables we define the perturbed function $C(B,\omega )$ and
the perturbed hierarchical Laplacian $L^{\omega }=L_{C(\omega )}.$ We study the
arithmetic means $\overline{\lambda }(\omega )$ of the $L^{\omega
}$-eigenvalues. Under some mild assumptions the normalized arithmetic means
$\big( \overline{\lambda }-\mathbb{E}\overline{\lambda }\big) /\sigma \big(
\overline{\lambda }\big) $ converge in law to the standard normal distribution.
In this note we study convergence in the total variation distance and estimate
the rate of convergence.

22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas