TL;DR
This paper explores the interplay between Quantum Field Theory and probability, highlighting how techniques like Renormalization Group and Gaussian Multiplicative Chaos enhance understanding in stochastic PDEs and Liouville CFT.
Contribution
It demonstrates novel applications of Quantum Field Theory methods to probability, particularly in stochastic PDEs and conformal field theory contexts.
Findings
Renormalization Group methods aid in analyzing stochastic PDEs
Gaussian Multiplicative Chaos provides insights into Liouville CFT
Cross-disciplinary techniques improve understanding of complex quantum-probability models
Abstract
I review some recent work where ideas and methods from Quantum Field Theory have proved useful in probability and vice versa. The topics discussed include the use of Renormalization Group theory in Stochastic Partial Differential Equations driven by space-time white noise and the use of the theory of Gaussian Multiplicative Chaos in the study of two dimensional Liouville Conformal Field theory.
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