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SUMMARY:Percolation\, long-range correlations and critical exponents on tr
 ansient graphs - Alexander Drewitz (Universität zu Köln)
DTSTART:20220524T130000Z
DTEND:20220524T140000Z
UID:TALK174956@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Percolation models have been playing a fundamental role in sta
 tistical physics for several decades by now. They had initially been inves
 tigated in the gelation of polymers during the 1940s by chemistry Nobel la
 ureate Flory and Stockmayer. From a mathematical point of view\, the birth
  of percolation theory was the introduction of Bernoulli percolation by Br
 oadbent and Hammersley in 1957\, motivated by research on gas masks for co
 al miners. One of the key features of this model is the inherent stochasti
 c independence which simplifies its investigation\, and which has lead to 
 deep mathematical results. During recent years\, the investigation of the 
 more realistic and at the same time more complex situation of percolation 
 models with long-range correlations has attracted significant attention.\n
 \nWe will exhibit some recent progress for the Gaussian free field with a 
 particular focus on the understanding of the critical parameters in the as
 sociated percolation models. What is more\, we also survey recent progress
  in the understanding of the model at criticality via its critical exponen
 ts as well as the universality in the local geometry of the underlying gra
 ph.\n\nThis talk is based on joint works with A. Prevost (U Cambridge) and
  P.-F. Rodriguez (Imperial College).
LOCATION:MR12\, Centre for Mathematical Sciences
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