Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Asymptotic properties of harmonic measures on homogeneous trees

Tom 118 / 2010

Colloquium Mathematicum 118 (2010), 525-537 MSC: Primary 60J10; Secondary 60B15. DOI: 10.4064/cm118-2-9

Streszczenie

Let ${\rm Aff} ({\mathbb T})$ be the group of isometries of a homogeneous tree ${\mathbb T}$ fixing an end of its boundary. Given a probability measure on ${\rm Aff} ({\mathbb T})$ we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.