BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Universality of directed polymers in the intermediate disorder reg
 ime - Julian Ransford (Cambridge)
DTSTART:20241015T130000Z
DTEND:20241015T140000Z
UID:TALK222829@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:The directed polymer was introduced by Huse and Henley as a mo
 del for the domain wall in a ferromagnetic Ising model with random bond im
 purities. This model depends on a parameter $\\beta$\, the inverse tempera
 ture. We consider the intermediate disorder regime\, which consists in tak
 ing $\\beta$ to depend on the length of the polymer 2n\, with $\\beta=n^{-
 \\alpha}$ for some $\\alpha>0$. In this regime\, there is a critical phase
  transition that happens at $\\alpha=1/4$. When $\\alpha > 1/4$\, the fluc
 tuations of the free energy are of order $n^{(1-4\\alpha)/4}$ and converge
  to a Gaussian. For $\\alpha < 1/4$\, it was conjectured that the polymer 
 should fall back in the Kardar—Parisi—Zhang universality class\, and t
 hat the fluctuations should instead be of order $n^{(1-4\\alpha)/3}$\, and
  converge after rescaling to the Tracy—Widom GUE distribution. In this t
 alk\, I will sketch a proof of this conjecture for $1/8 < \\alpha < 1/4$ f
 or arbitrary i.i.d weights with exponential moments\, using a kind of “l
 ocal chaos expansion”.
LOCATION:MR12
END:VEVENT
END:VCALENDAR