Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Quantitative Central Limit Theorem for the Euler-Poincar\'e
  Characteristic of Random Spherical Eigenfunctions   We establish here a Quantitative Central Limit Theorem (in Wasserstein
distance) for the Euler-Poincar\'{e} Characteristic of excursion sets of random
spherical eigenfunctions in dimension 2. Our proof is based upon a
decomposition of the Euler-Poincar\'{e} Characteristic into different
Wiener-chaos components: we prove that its asymptotic behaviour is dominated by
a single term, corresponding to the chaotic component of order two. As a
consequence, we show how the asymptotic dependence on the threshold level $u$
is fully degenerate, i.e., the Euler-Poincar\'{e} Characteristic converges to a
single random variable times a deterministic function of the threshold. This
deterministic function has a zero at the origin, where the variance is thus
asymptotically of smaller order. Our results can be written as an asymptotic
second-order Gaussian Kinematic Formula for the excursion sets of Gaussian
spherical harmonics.

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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat