BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Higher moments for the SHE in high dimensions and their phase tran
 sitions
DTSTART:20260414T101000
DTEND:20260415T110000
DTSTAMP:20260404T023418Z
UID:1d5e777d66d6edc919aece40a69c761bfdf267584fadd200f6c95d3a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Te-Chun Wang (EPFL)\nWe consider regularized versions of th
 e stochastic heat equation (SHE) in high dimensions $d\\geq 3$ and analyze
  their higher moments in the limit as the regularization is removed\, for 
 varying coupling constants that describe the strength of the driving noise
 . Motivated by recent results on the higher moments of the SHE in two dime
 nsions at $L^{2}$-criticality\, a natural question is whether the higher m
 oments of the SHE in high dimensions also converge at the $L^{2}$-critical
  point. Our main result gives a negative answer: in high dimensions\, the 
 higher moments diverge when the coupling constant belongs to a nontrivial 
 right-closed interval whose upper endpoint is the $L^{2}$-critical point. 
 In particular\, we obtain a sharp bound for the critical coupling constant
  at which the corresponding limiting higher moment undergoes a phase trans
 ition. As an application to the continuous directed polymer\, we derive a 
 sharp estimate for quantity believed to be closely related to the tail pro
 bability of the limiting partition function.
LOCATION:MA B2 485
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR