A note on Sarnak processes
Basic properties of stationary processes called Sarnak processes are studied. As an application, a combinatorial reformulation of Sarnak's conjecture on M{ö}bius orthogonality is provided.
math.DS↗
arXiv subjects
Thierry de La Rue
Publications and source records attributed to Thierry de La Rue.
M{ö}bius orthogonality in density for zero entropy dynamical systems
It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $μ$ stands for the arithmetic M{ö}bius function, then there exists a subset $A$ of integers depending only on the system, of logarithmic density one, such that for each $f$ continuous on $X$, $\frac1N \sum_{n\leq N} f(T^nx)μ(n) \to 0$ as $N\to\infty$, $N\in A$, uniformly in $x\in X$. In particular, the density version of M{ö}bius orthogonality holds.
math.DS↗