Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rare Events Are Nonperturbative: Primordial Black Holes From
  Heavy-Tailed Distributions   In recent years it has been noted that the perturbative treatment of the
statistics of fluctuations may fail to make correct predictions for the
abundance of primordial black holes (PBHs). Moreover, it has been shown in some
explicit single-field examples that the nonperturbative effects may lead to an
exponential tail for the probability distribution function (PDF) of
fluctuations responsible for PBH formation -- in contrast to the PDF being
Gaussian, as suggested by perturbation theory. In this paper, we advocate that
the so-called $\delta N$ formalism can be considered as a simple, yet
effective, tool for the nonperturbative estimate of the tail of the PDF. We
discuss the criteria a model needs to satisfy so that the results of the
classical $\delta N$ formalism can be trusted and most possible complications
due to the quantum nature of fluctuations can be avoided. As a proof of
concept, we then apply this method to a simple example and show that the tail
of the PDF can be even heavier than exponential, leading to a significant
enhancement of the PBH formation probability, compared with the predictions of
the perturbation theory. Our results, along with other related findings,
motivate invention of new, nonperturbative methods for the problem and open up
new ideas on generating PBHs with notable abundance.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph