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SUMMARY:Models of large-scale real-life networks - Bela Bollobas - Univers
 ity of Cambridge and University of Memphis
DTSTART:20100120T141500Z
DTEND:20100120T151500Z
UID:TALK22080@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:In the last fifty years or so\, much research has been done on
  various models\nof random graphs in mathematics\, computer science and ph
 ysics. Among the\nfamilies of models that mathematicians have worked on ov
 er the years\, two\nstand out: the mean-field models\, whose study was sta
 rted by Erd˝os and R´enyi\nin the late 1950s\, and the percolation model
 s\, based on lattices and lattice-like\ninfinite graphs\, introduced by Br
 oadbent and Hammersley at about the same\ntime. By now\, we have elaborate
  and deep theories of random subgraphs of\ncomplete graphs and of percolat
 ion on lattices.\n\nIt was realized only fairly recently that random graph
  models may be very\nimportant in the study of massive graphs that occur i
 n real life\, like the graph\nof the World Wide Web\, or various biologica
 l networks. These graphs are too\nbig to describe precisely\, and even if 
 we could get all the information about\nthem\, this information could not 
 be handled efficiently. It seems that the best\nwe can do is model them as
  well as we can\, and study the model. At the first\nsight it is surprisin
 g that the best models seem to be random graphs\, although\nthis is much l
 ess surprising if we realize that many of these graphs arise by a\nmixture
  of deterministic constructions and random decisions.\n\nIn the talk we sh
 all review a number of these models\, and present several results\nabout t
 hem\, including some I have obtained jointly with Oliver Riordan and\nSvan
 te Janson.
LOCATION:Lecture Theatre 1\, Computer Laboratory
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