Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cumulants asymptotics for the zeros counting measure of real Gaussian
  processes   We compute the exact asymptotics for the cumulants of linear statistics
associated with the zeros counting measure of a large class of real Gaussian
processes. Precisely, we show that if the underlying covariance function is
regular and square integrable, the cumulants of order higher than two of these
statistics asymptotically vanish. This result implies in particular that the
number of zeros of such processes satisfies a central limit theorem. Our
methods refines the recent approach by T. Letendre and M. Ancona and allows us
to prove a stronger quantitative asymptotics, under weaker hypotheses on the
underlying process. The proof exploits in particular the elegant interplay
between the combinatorial structures of cumulants and factorial moments in
order to simplify the determination of the asymptotics of nodal observables.
The class of processes addressed by our main theorem englobes as motivating
examples random Gaussian trigonometric polynomials, random orthogonal
polynomials and the universal Gaussian process with sinc kernel on the real
line, for which the asymptotics of higher moments of the number of zeros were
so far only conjectured.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
16
The categories of this paper are: stat
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The categories of this paper are: cmp-lg