Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions

Nimit Rana; Martina Hofmanova; Massimiliano Gubinelli

doi:10.1007/s40072-024-00328-x

Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions

Nimit Rana, Martina Hofmanova, Massimiliano Gubinelli

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we consider the elliptic stochastic quantization of the Høegh–Krohn EQFT in two dimensions. The first method is based on a path-wise coupling argument and PDE apriori estimates, while the second on estimates of the Malliavin derivative of the solution to the SQ equation.

Original language	English
Number of pages	39
Journal	Stochastic Partial Differential Equations: Analysis and Computations
DOIs	https://doi.org/10.1007/s40072-024-00328-x
Publication status	Published - 7 May 2024

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AB - We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we consider the elliptic stochastic quantization of the Høegh–Krohn EQFT in two dimensions. The first method is based on a path-wise coupling argument and PDE apriori estimates, while the second on estimates of the Malliavin derivative of the solution to the SQ equation.

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