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DTSTAMP:20260709T112200Z
DESCRIPTION:Terrorists never congregate in even numbers (and other strange 
 results in fragmentation-coalescence)\n\n\n	Abstract:\n\n\nThe rigorous mat
 hematical treatment of random fragmentation-coalescent models in the liter
 ature is difficult to find\, and perhaps for good reason. We examine two d
 ifferent types of random fragmentation-coalescent models which produce som
 ewhat unexpected results.\n\nThe first concerns an agent-based model in wh
 ich\, with a rate that depends on the configuration of the system\, agents
  coalesce into clusters that also fragment into their individual constitue
 nt membership. We consider the large-scale\, long-term behaviour of this s
 ystem in a similar spirit to recent use of such models to characterise the
  evolution of terrorist cells. Under appropriate assumptions we find an un
 usual behaviour\; the system displays stabilisation with clusters that onl
 y contain an odd number of individuals.\n\nOur second random fragmentation
 -coalescent model is described from the outset as an infinite exchangeable
  system of agents. We introduce a variant of Kingman’s Coalescent\, which 
 is Markov process on the space of exchangeable partitions of the natural n
 umbers\, in which blocks of the partition can fragment into their constitu
 ent singletons. We ask the simple question: “Does this model make sense wh
 en it begins with an infinite number of blocks?”. In other words we addres
 s the notion of the fragmentation-coalescent “coming down from infinity”. 
 Again\, we find an unusual behaviour\; depending on a counter-intuitive pa
 rameter regime\, the system may or may not be able to come down from infin
 ity.\n\nThis is joint work based on two papers with Steven Pagett\, Tim Ro
 gers and Jason Schweinsberg.\n\n\n	Speaker\n\n\nAndreas Kyprianou is a Prof
 essor in the Department of Mathematical Sciences at the University of Bath
 . His research interests include Branching Processes\, Branching Diffusion
 s and Superprocesses. Random Walks\, Brownian motion\, Levy processes and 
 Self-similar Markov processes\, Monte-Carlo simulation of stochastic proce
 sses\n
DTSTART:20181102T193000Z
DTEND:20181102T203000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Andreas Kyprianou 
URL:/mathstat/channels/event/andreas-kyprianou-291289
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