Random Matrix Product and Arithmetic Applications
speaker: Jordan Emme (Institut de Mathématique d'Orsay)abstract: In a work with Pascal Hubert, we study limit laws for some particular random matrix products and we give an arithmetic application: Let us denote by $s2$ the sum-of-digit function in base 2. We consider, for every pair of integers $a$ and $d$, the asymptotic density of the set of integers $n$ such that $s2(n+a)-s2(n)=d$. We denote this asymptotic density by $\mua(d)$. For every integer $a$, $mua$ is a probability measure on $\mathbb{Z}$. We show that for every shift-invariant ergodic probability measure on $\{0,1\}{\mathbb{N}}$, and for every integer sequence $(an)$ whose binary decomposition follow the prefixes of a generic point in $\{0,1\}{\mathbb{N}}$ for this measure, the probability measures $(mu{an})$ satisfy a central limit theorem. This is done by computing the characteristic functions of these measures, which are given by random matrix products.
timetable:
Fri 13 Apr, 10:30 - 11:20, Aula Dini
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