Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rare event process and entry times distribution for arbitrary null sets
  on compact manifolds   We establish the general equivalence between rare event process for arbitrary
continuous functions whose maximal values are achieved on non-trivial sets, and
the entry times distribution for arbitrary measure zero sets. We then use it to
show that the for differentiable maps on a compact Riemannian manifold that can
be modeled by Young's towers, the rare event process and the limiting entry
times distribution both converge to compound Poisson distributions. A similar
result is also obtained on Gibbs-Markov systems, for both cylinders and open
sets. We also give explicit expressions for the parameters of the limiting
distribution, and a simple criterion for the limiting distribution to be
Poisson. This can be applied to a large family of continuous observables that
achieve their maximum on a non-trivial set with zero measure.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
16
The categories of this paper are: stat