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UID:c406c7402582e8208924f325269059f2
CATEGORIES:Discrete Math
CREATED:20230125T142629
SUMMARY:Site percolation on planar graphs and circle packings
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: Color each vertex of an infinite graph blue with probability p an
 d red with probability 1-p, independently among vertices. For which values 
 of p is there an infinite connected component of blue vertices? The talk wi
 ll focus on this classical percolation problem for the class of planar grap
 hs. Recently, Itai Benjamini made several conjectures in this context, rela
 ting the percolation problem to the behavior of simple random walk on the g
 raph. We will explain how partial answers to Benjamini's conjectures may be
  obtained using the theory of circle packings. Among the results is the fac
 t that the critical percolation probability admits a universal lower bound 
 for the class of recurrent plane triangulations. Open problems will be emph
 asized. No previous knowledge on percolation or circle packings will be ass
 umed.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin: 0in;"><strong>Abstract:</strong> Color each vertex of an 
 infinite graph blue with probability p and red with probability 1-p, indepe
 ndently among vertices. For which values of p is there an infinite connecte
 d component of blue vertices? The talk will focus on this classical percola
 tion problem for the class of planar graphs.&nbsp;Recently, Itai Benjamini 
 made several conjectures in this context, relating the percolation problem 
 to the behavior of simple random walk on the graph. We will explain how par
 tial answers to Benjamini's conjectures may be obtained using the theory of
  circle packings. Among the results is the fact that the critical percolati
 on probability admits a universal lower bound for the class of recurrent pl
 ane triangulations.&nbsp;Open problems will be emphasized. No previous know
 ledge on percolation or circle packings will be assumed.</p>
CONTACT:Ron Peled - Tel Aviv University and Princeton University
DTSTAMP:20260828T185708
DTSTART;TZID=America/New_York:20230130T140000
DTEND;TZID=America/New_York:20230130T150000
SEQUENCE:0
TRANSP:OPAQUE
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