Limit theorems for conditioned non-generic Galton-Watson trees

Speaker: Igor Kortchemski

Date: Thu, Jun 14, 2012

Location: PIMS, University of British Columbia

Conference: PIMS-MPrime Summer School in Probability

Subject: Mathematics, Probability

Class: Scientific


We are interested in a particular type of subcritical Galton-Watson trees, which are called non-generic trees in the physics community. In contrast with the critical or supercritical case, it is known that condensation appears in large conditioned non-generic trees, meaning that with high probability there exists a unique vertex with macroscopic degree comparable to the total size of the tree. We investigate this phenomenon by studying scaling limits of such trees. In particular, we show that the height of such trees grows logarithmically in their size.