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DTSTAMP:20210922T041934Z
UID:1608046200@ist.ac.at
DTSTART:20201215T163000
DTEND:20201215T171500
DESCRIPTION:Speaker: Francesco Caravenna\nhosted by M. Beiglböck\, N. Bere
stycki\, L. Erdös\, J. Maas\, F. Toninelli\nAbstract: We consider the Kar
dar-Parisi-Zhang equation (KPZ) and the multiplicative Stochastic Heat Equ
ation (SHE) in two space dimensions\, driven by with space-time white nois
e. These PDEs are very singular and lack a solution theory\, so it is stan
dard to introduce a regularization - e.g. by convolving the noise with a s
mooth mollifier - and to investigate the behavior of the solutions when th
e regularization is removed. Interestingly\, these regularized solutions a
re closely linked to a much studied model in statistical mechanics\, the s
o-called directed polymer in random environment. Building on this link\, w
e show that a phase transition emerges\, as the noise strength is varied o
n a logarithmic scale. In the sub-critical regime\, the solutions of the r
egularized KPZ and SHE (suitably centered and rescaled) converge to an exp
licit Gaussian field\, the solution of an *additive* Stochastic Heat Equat
ion. We finally discuss the critical regime\, where many questions are ope
n. Based on joint works with Rongfeng Sun and Nikos Zygouras
LOCATION:Online via Zoom\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Francesco Caravenna: On the two-dimensional KPZ and Stochastic Heat
Equation
URL:https://talks-calendar.app.ist.ac.at/events/2994
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