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DTSTART:20200329T030000
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DTSTAMP:20200807T131840Z
UID:5b4d921122a41204310746@ist.ac.at
DTSTART:20200107T173000
DTEND:20200107T183000
DESCRIPTION:Speaker: Giacomo Di Gesù\nhosted by M. Beiglböck\, N. Beresty
cki\, L. Erdös\, J. Maas\nAbstract: We consider the Allen-Cahn equation o
n the one-dimensional torus\, perturbed by a small spacetime white noise.
The deterministic equation is a nonlinear PDE\, which can be seen as a gra
dient flow with respect to a double-well energy. If a small noise is added
\, the typical picture of a metastable dynamics emerges: the system quickl
y reaches a local equilibrium in one of the two wells\; this state endures
for an exponentially long time\, until a sufficiently large stochastic fl
uctuation enables the system to overcome the energetic barrier separating
the two wells. This behavior produces a slowdown in the relaxation to the
equilibrium measure\, reflected e.g. by an exponentially small spectral ga
p. In th alk I will present a technique which provides a formula for the p
recise asymptotic behavior of the spectral gap\, showing that the prefacto
r is given by a suitable Fredholm determinant. The formula shows that the
gap behaves like twice the inverse of the metastable transition time from
one well to the other.
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, IST Austria
ORGANIZER:boosthui@ist.ac.at
SUMMARY:An Eyring-Kramers formula for the spectral gap of the stochastic Al
len-Cahn equation
URL:https://talks-calendar.app.ist.ac.at/events/2470
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