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UID:20251008T052429EDT-75053Dtomz@132.216.98.100
DTSTAMP:20251008T092429Z
DESCRIPTION:Title: Globally centred snakes.\n\nAbstract: We consider a glob
 ally centred discrete snake on a Bienaymé tree with critical\, finite vari
 ance offspring distribution which satisfies a finite global variance condi
 tion. Making use of a discrete line-breaking construction from a recent pa
 per of Addario-Berry\, Blanc-Renaudie\, Donderwinkel\, Maazoun and Martin\
 , we give a new proof of convergence (under rescaling) to the Brownian sna
 ke driven by a Brownian excursion in the sense of finite-dimensional distr
 ibutions. The conditions required for tightness are a work in progress\, b
 ut we demonstrate the necessity of a natural tail-condition on the displac
 ements. This extends earlier results of various authors including Janson a
 nd Marckert for the case where the displacements are independent of the of
 fspring numbers\, and Marckert for the globally centred\, global finite va
 riance case restricted to bounded offspring distributions. Our results app
 ly\, in particular\, to give the convergence of a special discrete snake w
 hich gives the difference between the height process of such a Bienaymé tr
 ee and a constant multiple of its Łukasiewicz path\, when rescaled by n^{-
 1/4}.\n\nThis is joint work in progress with Louigi Addario-Berry\, Serte 
 Donderwinkel and Rivka Mitchell.\n\n \n
DTSTART:20240919T153000Z
DTEND:20240919T163000Z
LOCATION:Room 719A\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Christina Goldschmidt (Oxford Oxford University)
URL:/mathstat/channels/event/christina-goldschmidt-oxf
 ord-oxford-university-359781
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