A limit theorem for torus translation

TL;DR

This paper establishes a limit theorem for a specific observable with a singularity on the torus, advancing understanding of its statistical behavior.

Contribution

It introduces a new limit theorem for observables with singularities of type x^{-a} on the torus, which was not previously known.

Findings

Proves a limit theorem for singular observables on the torus

Characterizes the statistical distribution of the observable

Extends the theory of limit theorems to singular functions

Abstract

In this article, we prove a limit theorem for an observable on the torus with a singularity of type $x^{-a}$, where $0<a<1$.