Seminario EDP UAM-ICMAT
Renormalizing singular SPDEs via spectral gap inequalities
Ponente: Pablo Linares (UAM)Fecha: viernes 22 de noviembre de 2024 - 13:45Lugar: Aula Gris 2, ICMAT
Resumen:
In singular stochastic PDEs, approximations by mollification fail to converge due to the low regularity of the noise, which creates divergencies in some nonlinear terms.
“Renormalizing” the SPDE is removing such divergencies, adding divergent counterterms to the equation, in a way that convergence is restorted. Within the theory of regularity structures (Hairer 2014), we introduce a systematic method to tackle this problem based on the assumption that the noise satisfies a spectral gap inequality. This inequality is well-suited for our purpose for two reasons: On the one hand, the expectation of the noise functionals determines the counterterms, thus fitting a BPHZ-type choice of renormalization; on the other, the Mallivain/noise derivative of the functional controls the variance in a more regular space of modelled distributions which allows for reconstruction. This talk is based on joint work with Felix Otto, Markus Tempelmayr and Pavlos Tsatsoulis.
