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UID:20250802T102126EDT-0482RvlMnr@132.216.98.100
DTSTAMP:20250802T142126Z
DESCRIPTION:The new world of infinite random geometric graphs.\n\nThe infin
 ite random or Rado graph R has been of interest to graph theorists\, proba
 bilists\, and logicians for the last half-century. The graph R has many pe
 culiar properties\, such as its categoricity: R is the unique countable gr
 aph satisfying certain adjacency properties. Erdös and Rényi proved in 19
 63 that a countably infinite binomial random graph is isomorphic to R.\n	\n
 	Random graph processes giving unique limits are\, however\, rare. Recent j
 oint work with Jeannette Janssen proved the existence of a family of rando
 m geometric graphs with unique limits. These graphs arise in the normed sp
 ace $ell^n_infty$ \, which consists of $mathbb{R}^n$ equipped with the $L_
 infty$-norm. Balister\, Bollobás\, Gunderson\, Leader\, and Walters used 
 tools from functional analysis to show that these unique limit graphs are 
 deeply tied to the $L_infty$-norm. Precisely\, a random geometric graph on
  any normed\, finite-dimensional space not isometric $ell^n_infty$ gives n
 on-isomorphic limits with probability 1.With Janssen and Anthony Quas\, we
  have discovered unique limits in infinite dimensional settings including 
 sequences spaces and spaces of continuous functions. We survey these newly
  discovered infinite random geometric graphs and their properties.\n
DTSTART:20171214T203000Z
DTEND:20171214T213000Z
LOCATION:Room 2830\, CA\, Université Laval\, Pavillon Vachon
SUMMARY:Anthony Bonato\, Ryerson University
URL:/mathstat/channels/event/anthony-bonato-ryerson-un
 iversity-283304
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