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SUMMARY:Vertices of high degree in the preferential attachment tree - Lucz
 ak\, M (London School of Economics)
DTSTART:20110302T140000Z
DTEND:20110302T150000Z
UID:TALK30083@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The preferential attachment tree is the most basic model of ev
 olving web graphs. At each stage of the process\, a new vertex is added an
 d joined to one of the existing vertices\, with each vertex chosen with pr
 obability proportional to its current degree. In probability theory\, this
  is also known as a Yule process.\n\nMuch is known about this model\, incl
 uding the fact that the numbers of  vertices of each small degree follow a
  ``power law''. Here we study in detail the degree sequence of the prefere
 ntial attachment tree\, looking at the vertices of large degrees as well a
 s the numbers of vertices of each fixed degree.\n \nOur method is based on
  bounding martingale deviations\, using exponential supermartingales.\n\nT
 his is joint work with Graham Brightwell.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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