Sharp asymptotics for the Allen-Cahn equation in the limit of small noise and large volume – Giacomo di Gesù (Roma La Sapienza)


Aula Seminari


We consider the Allen-Cahn equation on a finite interval perturbed by space-time white noise. Keeping the size of the spatial domain fixed, the dynamics becomes metastable in the limit of vanishing noise. I will review some sharp metastability estimates in this regime and discuss how the invariant measure and long-time behavior is affected if one allows the system size to grow while the noise vanishes (joint work with L. Bertini and P. Buttà).

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