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SUMMARY:Dimension Dependence of Critical Phenomena in Percolation (3/6)
DTSTART:20250519T080000Z
DTEND:20250519T100000Z
DTSTAMP:20260423T111200Z
UID:indico-event-14115@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Thomas Hutchcroft (California Institute of Technolog
 y)\n\nAtttention : Les deux premières Leçons auront lieu à l'IMO\, Amph
 ithéâtre Yoccoz\, le 16 mai à 10h et à 14h\nRetrouvez toutes ces infor
 mations sur le site de la Fondation Mathématique Jacques Hadamard :\nhttp
 s://www.fondation-hadamard.fr/fr/evenements/cours-avances/\nAbstract:\nIn 
 Bernoulli bond percolation\, we delete or retain each edge of a graph inde
 pendently at random with some retention parameter p and study the geometry
  of the connected components (clusters) of the resulting subgraph. For lat
 tices of dimension d>1\, percolation has a phase transition\, with a infin
 ite cluster emerging at a critical probability pc(d). It is believed that 
 critical percolation at and near the critical probability exhibits rich\, 
 fractal-like geometry that is expected to be approximately independent of 
 the choice of lattice but highly dependent on the dimension d. In particul
 ar\, various qualitative distinctions are expected between the low dimensi
 onal case d<6\, the high-dimensional case d>6\, and the critical case d=6\
 , but this remains poorly understood particularly in dimensions d=3\,4\,5\
 ,6.In this course\, I will give an overview of of what is known about crit
 ical percolation\, focussing on recent advances in long-range and hierarch
 ical models for which various aspects of intermediate-dimensional critical
  phenomena can now be understood rigorously.\n \n\nhttps://indico.math.cn
 rs.fr/event/14115/
LOCATION:Centre de conférences Marilyn et James Simons (IHES)
URL:https://indico.math.cnrs.fr/event/14115/
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