BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Invariant measure of the stochastic Allen-Cahn equation: the regim
 e of small noise and large system size - Weber\, H (University of Warwick)
DTSTART:20120914T135000Z
DTEND:20120914T144000Z
UID:TALK39754@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We study the invariant measure of the one-dimensional stochast
 ic Allen-Cahn equation for a small noise strength and a large but finite s
 ystem. We endow the system with inhomogeneous Dirichlet boundary condition
 s that enforce at least one transition from -1 to 1. We are interested in 
 the competition between the ``energy'' that should be minimized due to the
  small noise strength and the ``entropy'' that is induced by the large sys
 tem size. \n\nOur methods handle system sizes that are exponential with re
 spect to the inverse noise strength\, up to the ``critical'' exponential s
 ize predicted by the heuristics. We capture the competition between energy
  and entropy through upper and lower bounds on the probability of extra tr
 ansitions between +1 and -1. These bounds are sharp on the exponential sca
 le and imply in particular that the probability of having one and only one
  transition from -1 to +1 is exponentially close to one. In addition\, we 
 show that the position of the transition layer is uniformly distributed ov
 er the system on scales larger than the logarithm of the inverse noise str
 ength. \n\nOur arguments rely on local large deviation bounds\, the strong
  Markov property\, the symmetry of the potential\, and measure-preserving 
 reflections. \n
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR