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

Massimiliano Gubinelli, Martina Hofmanová and Nimit Rana

First issued 19 May 2023 · PDF

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 (or $\exp (\alpha \phi)_2$) 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.

Versions

1. Version 2 (arXiv v2) current
   14 April 2024
   arXiv comments: 30 pages - accepted version
   PDF · LaTeX source · files and digests · arXiv:2305.12017
2. Version 1 (arXiv v1)
   19 May 2023
   arXiv comments: 28 pages
   PDF · TeXmacs source · files and digests · arXiv:2305.12017

Cite

Massimiliano Gubinelli, Martina Hofmanová and Nimit Rana. Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions. Papers of Massimiliano Gubinelli, 2023, version 2. https://mgubi.org/papers/paper/correlations-decay-exponential/

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