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SUMMARY:Reza Gheissari (U.C. Berkeley)
DTSTART:20200619T170000Z
DTEND:20200619T180000Z
DTSTAMP:20260423T022713Z
UID:PatC/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/7/">Cub
 e-root fluctuations and Tracy--Widom tails in critically pre-wetted Ising 
 interfaces</a>\nby Reza Gheissari (U.C. Berkeley) as part of Probability a
 nd the City Seminar\n\n\nAbstract\nConsider the 2D Ising model at low temp
 erature on an $N\\times N$ box with minus boundary conditions on the botto
 m and plus boundary conditions on the other three sides\, in the presence 
 of an external field $\\lambda \\ge 0$. Velenik (2004) proved that in the 
 \\emph{critical pre-wetting} regime of $\\lambda_N \\sim c/N$\, the area c
 onfined by the interface is $N^{\\frac{4}{3}+o(1)}$. Since then more refin
 ed features of such interfaces---which have been conjectured to converge t
 o the Ferrari--Spohn diffusion in critically sized $N^{2/3}\\times N^{1/3}
 $ windows--- have only been proven for approximations given by random walk
 s under area tilts. \n\nI will discuss recent work with Shirshendu Ganguly
  obtaining a more refined understanding of the local and global geometry o
 f the Ising interface in the critical pre-wetting regime. As part of this\
 , we find that its height fluctuations are truly of order $N^{1/3}$\, and 
 when they are rescaled by $N^{-1/3}$ they have $\\exp( - \\Theta(x^{3/2}))
 $ right tails reminiscent of the Tracy--Widom distribution.\n
LOCATION:https://researchseminars.org/talk/PatC/7/
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