Zusammenfassung für den Vortrag am 22.05.2018 (15:15 Uhr)Oberseminar ANALYSIS - PROBABILITY
Martina Hofmanova (TU Berlin)
Global solutions to elliptic and parabolic Φ4 models in Euclidean space
I will present some recent results on global solutions to singular SPDEs on ℝd with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions d = 4,5 and in the parabolic setting for d = 2,3. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum ﬁeld theories. The parabolic equations are related to the Φd4 Euclidean quantum ﬁeld theory via Parisi–Wu stochastic quantization, while the elliptic equations are linked to the Φd−24 Euclidean quantum ﬁeld theory via the Parisi–Sourlas dimensional reduction mechanism. We prove existence for the elliptic equations and existence, uniqueness and coming down from inﬁnity for the parabolic equations. Join work with Massimiliano Gubinelli.