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SUMMARY:A random walk approach to high-dimensional critical phenomena
DTSTART:20251008T150000
DTEND:20251008T161600
DTSTAMP:20260527T185704Z
UID:988f5313a1f0d75e86fd5ed158c2673b19bcd86c516baf8db6b07d48
CATEGORIES:Conferences - Seminars
DESCRIPTION:Romain Panis                \nOne of the main 
 goals of statistical mechanics is to understand critical phenomena of latt
 ice models. This can be achieved by computing the so-called critical expon
 ents\, which govern algebraic scaling near or at the critical point. This 
 task is generally impossible due to the intricate interplay between the sp
 ecific features of the models and the geometry of the graphs on which they
  are defined. A striking observation was made in the 20th century: above t
 he upper critical dimension d_c\, the geometry becomes inessential and cri
 tical exponents adopt their mean-field values (as on Cayley trees or compl
 ete graphs).\n\nClassical approaches—renormalization group\, differentia
 l inequalities with reflection positivity\, and the lace expansion—are p
 owerful yet model-specific and technically heavy. We revisit the study of 
 the mean-field regime and introduce a unified\, probabilistic framework th
 at applies across perturbative settings\, including weakly self-avoiding w
 alk (d>4)\, spread-out Bernoulli percolation (d>6)\, and one- and two-comp
 onent spin models (d>4).\n\nBased on ongoing works with Hugo Duminil-Copin
 \, Aman Markar\, and Gordon Slade.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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