Bogdan Stankov

Ecole Normale Supérieure de Paris | ENS · Département de Mathématiques et Applications

We prove an inequality, valid on any finitely generated group with a fixed finite symmetric generating set, involving the growth of successive balls, and the average length of an element in a ball. It generalizes recent improvements of the Coulhon Saloff-Coste inequality. We reformulate the inequality in terms of the F{\o}lner function; in the case...

We calculate the exact values of the F{\o}lner function of the lamplighter group for the standard generating set, as well as the F{\o}lner sets that give rise to it. F{\o}lner functions encode the isoperimetric properties of amenable groups and have previously been studied up to asymptotic equivalence (that is to say, independently of the choice of...

On étudie les marches aléatoires sur les groupes, et plus généralement les marches induites par des mesures sur des groupes. On cherche à comprendre leur comportement à l'infini, surtout en terme du non-trivialité de leur bords de Poisson. On s'intéresse en particulier aux sous-groupes de H(ℤ), y compris le groupe de Thompson F. Le groupe H(ℤ) est...

We consider a transitive action of a finitely generated group G and the Schreier graph \(\varGamma \) defined by this action for some fixed generating set. For a probability measure \(\mu \) on G with a finite first moment, we show that if the induced random walk is transient, it converges towards the space of ends of \(\varGamma \). As a corollary...

We give sufficient conditions for the non-triviality of the Poisson boundary of random walks on $H(\mathbb{Z})$ and its subgroups. The group $H(\mathbb{Z})$ is the group of piecewise projective homeomorphisms over the integers defined by Monod. For a finitely generated subgroup $H$ of $H(\mathbb{Z})$, we prove that either $H$ is solvable, or every...

We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ it defines. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the induced random walk is transient, it converges towards the space of ends of $\Gamma$. As a corollary we obtain that for a probability measure on Thompson'...

We give sufficient conditions for the non-triviality of the Poisson boundary of random walks on $H(\mathbb{Z})$ and its subgroups. The group $H(\mathbb{Z})$ is the group of piecewise projective homeomorphisms over the integers defined by Monod. For a finitely generated subgroup $H$ of $H(\mathbb{Z})$, we prove that either $H$ is solvable, or every...