Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Fibonacci numbers and extreme value laws for the R\'enyi map   In this paper we prove an extreme value law for a stochastic process obtained
by iterating the R\'enyi map $x \mapsto \beta x \pmod 1$, where we assume that
$\beta>1$ is an integer. Haiman (2018) derived a recursion formula for the
Lebesgue measure of threshold exceedance sets. We show how this recursion
formula is related to a rescaled version of the $k$-generalized Fibonacci
sequence. For the latter sequence we derive a Binet formula which leads to a
closed-form expression for the distribution of partial maxima of the stochastic
process. The proof of the extreme value law is completed by deriving sharp
bounds for the dominant root of the characteristic polynomial associated with
the Fibonacci sequence.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th