Seminarium:
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca:
Longmin Wang (Uniwersytet w Nankai, Chiny)
Data:
czwartek, 18. Kwiecień 2019 - 12:15
Sala:
602
Opis:
Let $\Gamma$ be a nonelementary hyperbolic group
equipped with a word metric. Consider a branching random walk (BRW)
on $\Gamma$ with mean offspring $\lambda < \infty$ and let $\rho$
be the spectral radius of the base motion. It is known that,
if and only if $\lambda > \rho^{-1}$, the BRW is recurrent in the sense that
every point is visited infinitely often by the particles in BRW.
In this talk, we focus on the transient regime $\lambda \in [1,\, \rho^{-1}]$
and study the critical behavior for the volume growth rate and
the Hausdorff dimension of the limit set of BRW. More precisely,
we prove that both of them exhibit phase transitions at $\lambda = \rho^{-1}$
and have critical exponent $1/2$. The talk is based on a joint work with
Z. Shi, V. Sidoravicius and K. Xiang.