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DTSTAMP:20260308T102903Z
SUMMARY:Rivka Mitchell (Oxford): Discrete Snakes with Globally Centered Dis
 placements
DESCRIPTION:Title\nDiscrete Snakes with Globally Centered Displacements\nAb
 stract\n\n\nWe consider certain size-conditioned critical Bienaymé trees\
 , in which each vertex is endowed with a spatial location that is a random
  displacement away from their parent’s location. By construction\, the p
 ositions along each vertex’s lineage form a random walk. It is convenien
 t to encode the genealogy and spatial locations using a path-valued proces
 s called the discrete snake. We prove that under a global finite variance 
 and a tail behaviour assumption on the displacements\, any globally center
 ed discrete snake on a Bienaymé tree whose offspring distribution is cri
 tical and admits a finite third moment has the Brownian snake driven by a 
 normalised Brownian excursion as its scaling limit. Our proof relies on tw
 o perspectives of Bienaymé trees. To prove convergence of finite dimensi
 onal distributions we rely on a line-breaking construction from a recent p
 aper of Addario-Berry\, Blanc-Renaudie\, Donderwinkel\, Maazoun and Martin
 . To prove tightness\, we adapt a method used by Haas and Miermont in the 
 context of height functions of Markov branching trees.\n\nThis is based on
  joint work in progress with Louigi Addario-Berry\, Serte Donderwinkel\, a
 nd Christina Goldschmidt.\n\n \n\nPlease note that the seminar will take 
 place in person in room 144 of Huxley Building.\n\nClick here to get to th
 e Junior Analysis Seminar webpage.
URL:https://www.imperial.ac.uk/events/188603/rivka-mitchell-oxford-discrete
 -snakes-with-globally-centered-displacements/
DTSTART;TZID=Europe/London:20250205T140000
DTEND;TZID=Europe/London:20250205T150000
LOCATION:144\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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