A temporal central limit theorem for irrational rotations
par
Salle de conférence
LJAD
Dynamical systems are deterministic systems. However, in chaotic systems where the entropy is positive, the ergodic sums often behave similarly to the sums of independent random variables and satisfy the spatial central limit theorems (CLT).
In zero-entropy systems, the spatial CLT often fails due to the lack of (fast) mixing properties. But in some cases, such as irrational rotations of bounded type, we can retrieve the central limit theorem if we study single orbit statistics, where we fix the starting point and randomise time, hence the word “temporal”. In this talk, I will present an ongoing joint work with Bromberg and Ulcigrai, where we generalise their method of coding and Markov chains to obtain a temporal central limit theorem for a broader class of observables over bounded irrational rotations.