Theoretical Statistics and Mathematics Unit, ISI Delhi

August 19, 2020 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Partha Pratim Ghosh,
ISI Delhi

Title:
Large Deviations for the Right-Most Position of a Last Progeny Modified Branching Random Walk.

Abstract of Talk

We consider a last progeny modified version of the branching random walk (M-BRW) where the particles at the last generation are given certain i.i.d. displacements which may be different from the increments. Under very minimal assumptions we derive a large deviation principle for the position of the new rightmost particle in this *M-BRW.* We also complete the derivation of large deviation principle for the position of the rightmost particle in the BRW that was left unsolved by Gantert and Hofelsauer and compare it with that of the M-BRW. It turns out that the rate functions coincide up to a constant depending on the displacements we added at the last generation.