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SUMMARY:Higher moments for the SHE in high dimensions and their phase tran
 sitions
DTSTART:20260331T101000
DTEND:20260331T110000
DTSTAMP:20260525T043259Z
UID:f6bcf9287bd2abfb70b159e5d6c9832a491551b5f4459941fab1117d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Te-Chun Wang (EPFL)\n\nWe consider regularized versions of 
 the stochastic heat equation (SHE) in high dimensions $d\\geq 3$ and analy
 ze their higher moments in the limit as the regularization is removed\, fo
 r varying coupling constants that describe the strength of the driving noi
 se. Motivated by recent results on the higher moments of the SHE in two di
 mensions at $L^{2}$-criticality\, a natural question is whether the higher
  moments of the SHE in high dimensions also converge at the $L^{2}$-critic
 al point. Our main result gives a negative answer: in high dimensions\, th
 e higher moments diverge when the coupling constant belongs to a nontrivia
 l right-closed interval whose upper endpoint is the $L^{2}$-critical point
 . In particular\, we obtain a sharp bound for the critical coupling consta
 nt at which the corresponding limiting higher moment undergoes a phase tra
 nsition. As an application to the continuous directed polymer\, we derive 
 a sharp estimate for quantity believed to be closely related to the tail p
 robability of the limiting partition function.
LOCATION:MA B2 485
STATUS:CONFIRMED
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