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SUMMARY:A growth-fragmentation found in the cone excursions of Brownian mo
 tion (and in the quantum disc) - Alex Watson (University College London)
DTSTART:20241016T130000Z
DTEND:20241016T140000Z
UID:TALK221653@talks.cam.ac.uk
DESCRIPTION:Consider a Brownian motion constrained to remain within a cone
  in theplane\, and conditioned to exit it at its apex. As it explores this
 space\, its path can be divided into sections living within smallersubcone
 s with random apexes: cone excursions. Cutting out theseexcursions produce
 s a process with jumps\, and the procedure can beiterated indefinitely wit
 hin the cut-out sections. What emerges is agrowth-fragmentation\, a type o
 f branching process with infiniteactivity. We demonstrate this and charact
 erise the law of thegrowth-fragmentation for a particular choice of apex a
 ngle. Theresulting process can be seen as describing the boundary lengths 
 ofcertain SLE curves drawn on a quantum disc\, and mirrors paralleldevelop
 ments in the field of random planar maps. A key element in thework is an i
 nteresting pathwise construction of the 3/2-stable processconditioned to s
 tay positive.\nThis is joint work with Ellen Powell (Durham) and William D
 a Silva (Vienna).
LOCATION:Seminar Room 2\, Newton Institute
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