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SUMMARY:A growth-fragmentation found in the cone excursions of Brownian mo
 tion - Alex Watson (UCL)
DTSTART;VALUE=DATE-TIME:20260223T140000Z
DTEND;VALUE=DATE-TIME:20260223T150000Z
UID:https://talks.ox.ac.uk/talks/id/66f3a797-ac66-4db8-ae1c-07e1b3d1a551/
DESCRIPTION:Consider a Brownian motion constrained to remain within a cone
  in the plane\, and conditioned to exit it at its apex. As it explores thi
 s space\, its path can be divided into sections living within smaller subc
 ones with random apexes: cone excursions. Cutting out these excursions pro
 duces a process with jumps\, and the procedure can be iterated indefinitel
 y within the cut-out sections. What emerges is a growth-fragmentation\, a 
 type of branching process with infinite activity. We demonstrate this and 
 characterise the law of the growth-fragmentation for a particular choice o
 f apex angle. The resulting process can be seen as describing the boundary
  lengths of certain SLE curves drawn on a quantum disc\, and mirrors paral
 lel developments in the field of random planar maps. A key element in the 
 work is an interesting pathwise construction of the 3/2-stable process con
 ditioned to stay positive.\n\nThis is joint work with Ellen Powell (Durham
 ) and William Da Silva (Vienna).\nSpeakers:\nAlex Watson (UCL)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/66f3a797-ac66-4db8-ae1c-07e1b3d1a551/
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DESCRIPTION:Talk:A growth-fragmentation found in the cone excursions of Br
 ownian motion - Alex Watson (UCL)
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