BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antar Bandyopadhyay (Indian Statistical Institute\, Delhi) DTSTART:20200812T090000Z DTEND:20200812T095000Z DTSTAMP:20260404T132232Z UID:BPS/2 DESCRIPTION:Title: A Last Progeny Modified Branching Random Walk\nby Antar Bandyopadhy ay (Indian Statistical Institute\, Delhi) as part of Bangalore Probability Seminar\n\n\nAbstract\nIn this work\, we consider a modification of the u sual Branching Random Walk (BRW)\, where at the n-th step we give certain i.i.d. displacements to each individuals\, which may be different from th e driving increment distribution. Depending on the value a parameter\, we classify the model in three distinct cases\, namely\, the boundary case\, below the boundary case and above the boundary case. Under very minimal a ssumptions on the underlying point process of the increments\, we show tha t at the boundary case\, the maximum displacement converges to a limit aft er only an appropriate centering\, which is of the form c1 n - c2log n. We give explicit formula for the constants c1 and c2 and show that c1 is exa ctly same\, while c2 is 1/3 of the corresponding constants of the usual B RW. We also characterize the limiting distribution. We further show that b elow the boundary the logarithmic correction term is absent. For above the boundary case\, we have only partial result which indicates a possible ex istence of the logarithmic correction in the centering with exactly same constant as that of the classical BRW. Our proofs are based on a novel met hod of coupling with a more well studied process known as the smoothing t ransformation\, which is used in various non-parametric statistical metho ds.\n LOCATION:https://stable.researchseminars.org/talk/BPS/2/ END:VEVENT END:VCALENDAR