Central limit theorem for products of toral automorphisms

Details Central limit theorem for products of toral automorphisms Central limit theorem for products of toral automorphisms

2010-06-21

arxiv.org/abs/1006.4051v1

Mathematics

Probability

Scientific paper

Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of "multiplicative systems" of Koml\`os can be used to prove a Central Limit Theorem for the sums $\sum_{k=1}^n f(\tau_k \circ \tau_{k-1} \cdots \circ \tau_1 x)$ if $f$ is a H\"older function on $\mathbb{T}^d$. These conditions hold for $2\times 2$ matrices with positive coefficients. In dimension $d$ they can be applied when $A_n= A_n(\omega)$, with independent choices of $A_n(\omega)$ in a finite set of matrices $\in SL(d, \mathbb{Z})$, in order to prove a "quenched" CLT.

Affiliated with

Also associated with

No associations

Rating

Central limit theorem for products of toral automorphisms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Central limit theorem for products of toral automorphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Central limit theorem for products of toral automorphisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601248