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UID:20260408T063954EDT-4040vnktTG@132.216.98.100
DTSTAMP:20260408T103954Z
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	Ra
 ndom graph processes giving unique limits are\, however\, rare. Recent joi
 nt work with Jeannette Janssen proved the existence of a family of random 
 geometric graphs with unique limits. These graphs arise in the normed spac
 e $ell^n_infty$ \, which consists of $mathbb{R}^n$ equipped with the $L_in
 fty$-norm. Balister\, Bollobás\, Gunderson\, Leader\, and Walters used to
 ols from functional analysis to show that these unique limit graphs are de
 eply tied to the $L_infty$-norm. Precisely\, a random geometric graph on a
 ny normed\, finite-dimensional space not isometric $ell^n_infty$ gives non
 -isomorphic limits with probability 1.With Janssen and Anthony Quas\, we h
 ave discovered unique limits in infinite dimensional settings including se
 quences spaces and spaces of continuous functions. We survey these newly d
 iscovered 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:https://www.mcgill.ca/channels/channels/event/anthony-bonato-ryerson-un
 iversity-283304
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