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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20250203T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-shlomo-hoory
SUMMARY:Algebraic Graph Theory-Shlomo Hoory
CLASS:PUBLIC
DESCRIPTION:TITLE: Entropy and the growth rate of universal covering trees\
 n\nSPEAKER:\n Shlomo Hoory\n\nAFFILIATION:\n Tel-Hai College\n\nLOCATION:\
 n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT:This work studi
 es the relation between two graph parameters\,\nrho and Lambda. For an und
 irected graph G\,  rho(G) is the growth rate\nof its universal covering t
 ree\, while Lambda(G) is a weighted\ngeometric average of the vertex degre
 e minus one\, corresponding to the\nrate of entropy growth for the non-bac
 ktracking random walk (NBRW). It\nis well known that rho >= Lambda for all
  graphs\, and that graphs with\nrho = Lambda exhibit some special properti
 es. In this work we derive\nan easy to check\, necessary and sufficient co
 ndition for the equality\nto hold. Furthermore\, we show that the variance
  of the number of\nrandom bits used by a length l NBRW is O(1) if rho = La
 mbda and\nOmega(l) if rho > Lambda. As a consequence we exhibit infinitely
  many\nnon-trivial examples of graphs with rho = Lambda.\n\nJoint work wit
 h Idan Eisner\, Tel-Hai College\, Israel.
DTSTAMP:20260403T013449Z
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