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SUMMARY:A random walk approach to high-dimensional critical phenomena
DTSTART:20251008T150000
DTEND:20251008T160000
DTSTAMP:20260916T083808Z
UID:b9e4296e2e4588454b66562b5db17117d1ce70d44b98916cae3d6751
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professor Romain Panis   \nOne of the main goals of statist
 ical mechanics is to understand critical phenomena of lattice models. This
  can be achieved by computing the so-called critical exponents\, which g
 overn algebraic scaling near or at the critical point. This task is genera
 lly impossible due to the intricate interplay between the specific feature
 s of the models and the geometry of the graphs on which they are defined. 
 A striking observation was made in the 20th century: above the upper crit
 ical dimension d_c\, the geometry becomes inessential and critical expone
 nts adopt their mean-field values (as on Cayley trees or complete graphs
 ).\n\nClassical approaches—renormalization group\, differential inequali
 ties with reflection positivity\, and the lace expansion—are powerful ye
 t model-specific and technically heavy. We revisit the study of the mean-f
 ield regime and introduce a unified\, probabilistic framework that applies
  across perturbative settings\, including weakly self-avoiding walk (d>4)\
 , spread-out Bernoulli percolation (d>6)\, and one- and two-component spin
  models (d>4).\n\nBased on ongoing works with Hugo Duminil-Copin\, Aman Ma
 rkar\, and Gordon Slade.
LOCATION:CM1517
STATUS:CONFIRMED
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