APS
Speaker: Aditya DSS, IIT Bombay
Host: Ayan Bhattacharya
Title: Growth of regularly varying branching random walks
Time, day and date: 8:15:00 AM – 9:15:00 AM, Tuesday, September 08
Venue: Conference Room
Abstract: We consider branching random walks (BRWs) with real-valued displacements having regularly varying tails, allowing the tail behavior of the displacements to vary across generations. We study the exponential growth of the BRW through its maximal position when the underlying genealogical tree is generated by a supercritical Bienaymé–Galton–Watson process with finite mean. We show that the growth exhibits a phase transition depending on the indices of regular variation of the displacement tails. We further investigate the fluctuations of the maximal position by establishing a weak limit for the appropriately normalized maximal position in the (n)-th generation.