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:20260421T173248Z UID:BPS/2 DESCRIPTION:Title: A La st Progeny Modified Branching Random Walk\nby Antar Bandyopadhyay (Ind ian Statistical Institute\, Delhi) as part of Bangalore Probability Semina r\n\n\nAbstract\nIn this work\, we consider a modification of the usual Br anching Random Walk (BRW)\, where at the n-th step we give certain i.i.d. displacements to each individuals\, which may be different from the drivi ng increment distribution. Depending on the value a parameter\, we classi fy the model in three distinct cases\, namely\, the boundary case\, below the boundary case and above the boundary case. Under very minimal assumpti ons on the underlying point process of the increments\, we show that at th e boundary case\, the maximum displacement converges to a limit after only an appropriate centering\, which is of the form c1 n - c2log n. We give e xplicit formula for the constants c1 and c2 and show that c1 is exactly sa me\, while c2 is 1/3 of the corresponding constants of the usual BRW. We also characterize the limiting distribution. We further show that below th e boundary the logarithmic correction term is absent. For above the bounda ry case\, we have only partial result which indicates a possible existence of the logarithmic correction in the centering with exactly same constan t as that of the classical BRW. Our proofs are based on a novel method of coupling with a more well studied process known as the smoothing transfor mation\, which is used in various non-parametric statistical methods.\n LOCATION:https://researchseminars.org/talk/BPS/2/ END:VEVENT END:VCALENDAR