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DTSTART:20260329T030000
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DTSTAMP:20260425T051650Z
UID:684ad716936b6957954385@ist.ac.at
DTSTART:20260112T160000
DTEND:20260112T170000
DESCRIPTION:Speaker: Romain Panis\nhosted by Laszlo Erdös & Jan Maas\nAbst
 ract: One of the main goals of statistical mechanics is to understand crit
 ical phenomena of lattice models. This can be achieved by computing the so
 -called critical exponents\, which govern algebraic scaling near or at t
 he critical point. This task is generally impossible due to the intricate 
 interplay between the specific features of the models and the geometry of 
 the graphs on which they are defined. A striking observation was made in t
 he 20th century: above the upper critical dimension d_c\, the geometry b
 ecomes inessential and critical exponents adopt their mean-field values 
 (as on Cayley trees or complete graphs).Classical approaches—renormaliza
 tion group\, differential inequalities with reflection positivity\, and th
 e lace expansion—are powerful yet model-specific and technically heavy. 
 We revisit the study of the mean-field regime and introduce a unified\, pr
 obabilistic framework that applies across perturbative settings\, includin
 g weakly self-avoiding walk (d>4)\, spread-out Bernoulli percolation (d>6)
 \, and one- and two-component spin models (d>4).Based on ongoing works wit
 h Hugo Duminil-Copin\, Aman Markar\, and Gordon Slade.
LOCATION:Central Bldg / O1 / Mondi 2a (I01.O1.008)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Romain Panis: A random walk approach to high-dimensional critical p
 henomena
URL:https://talks-calendar.ista.ac.at/events/6225
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