BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Invariant measure of the stochastic Allen-Cahn equ
ation: the regime of small noise and large system
size - Weber\, H (University of Warwick)
DTSTART;TZID=Europe/London:20120914T145000
DTEND;TZID=Europe/London:20120914T154000
UID:TALK39754AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39754
DESCRIPTION:We study the invariant measure of the one-dimensio
nal stochastic Allen-Cahn equation for a small noi
se strength and a large but finite system. We endo
w the system with inhomogeneous Dirichlet boundary
conditions that enforce at least one transition f
rom -1 to 1. We are interested in the competition
between the ``energy'' that should be minimized du
e to the small noise strength and the ``entropy''
that is induced by the large system size. \n\nOur
methods handle system sizes that are exponential w
ith respect to the inverse noise strength\, up to
the ``critical'' exponential size predicted by the
heuristics. We capture the competition between en
ergy and entropy through upper and lower bounds on
the probability of extra transitions between +1 a
nd -1. These bounds are sharp on the exponential s
cale 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 over the system on scales la
rger than the logarithm of the inverse noise stren
gth. \n\nOur arguments rely on local large deviati
on bounds\, the strong Markov property\, the symme
try of the potential\, and measure-preserving refl
ections. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR