Large deviations for the Φ43 measure via Stochastic Quantisation
A talk in the Cluster Group Stochastic Analysis series by
Avi Mayorcas
| Abstract: | The Φ43 measure is one of the easiest non-trivial examples
of a Euclidean quantum field theory (EQFT) whose rigorous construction
in the 1970s has been one of the celebrated achievements of the
constructive QFT community. In recent years, progress in the field of
singular stochastic PDEs, initially by the theory of regularity
structures, has allowed to construct the Φ43 EQFT as the invariant
measure of a previously ill-posed Langevin dynamics—a strategy
originally proposed by Parisi and Wu (’81) under the name stochastic
quantization. In this talk, I will demonstrate that the same idea also
allows for the transference of large deviation principles for the Φ43
dynamics, obtained by Hairer and Weber (’15), to the corresponding
EQFT. Our strategy is inspired by earlier work of Sowers (’92) and
Cerrai and Röckner (’05) for non-singular dynamics and potentially
also applies to other EQFT measures. The talk is based on joint work
with Tom Klose (University of Warwick). |