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SUMMARY:The phase transition in bounded-size Achlioptas processes - Lutz W
 arnke (Cambridge)
DTSTART:20151124T163000Z
DTEND:20151124T173000Z
UID:TALK62257@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Perhaps the best understood phase transition is that in the co
 mponent structure of the uniform random graph process introduced by Erdˆs
  and RÈnyi around 1960.\nSince the model is so fundamental\, it is very i
 nteresting to know which features of this phase transition are specific to
  the model\, and which are `universal'\, at least within some larger class
  of processes.\nAchlioptas process\, a class of variants of the Erdˆs-RÈ
 nyi process that are easy to define but difficult to analyze\, have been e
 xtensively studied from this point of view. \nHere\, settling a number of 
 conjectures and open problems\, we show that all `bounded-size' Achlioptas
  processes share many key features of the Erdˆs-RÈnyi phase transition (
 in particular the asymptotic behaviour of the size of the largest componen
 t above and below the critical window). We do not expect this to hold for 
 Achlioptas processes in general. \nThis is joint work with Oliver Riordan.
  \n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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