随机量化中的相关性衰减：二维指数欧氏场

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-05-07 DOI:10.1007/s40072-024-00328-x

Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana

{"title":"随机量化中的相关性衰减：二维指数欧氏场","authors":"Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana","doi":"10.1007/s40072-024-00328-x","DOIUrl":null,"url":null,"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.","PeriodicalId":48569,"journal":{"name":"Stochastics and Partial Differential Equations-Analysis and Computations","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions\",\"authors\":\"Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana\",\"doi\":\"10.1007/s40072-024-00328-x\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":48569,\"journal\":{\"name\":\"Stochastics and Partial Differential Equations-Analysis and Computations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-05-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics and Partial Differential Equations-Analysis and Computations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40072-024-00328-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Partial Differential Equations-Analysis and Computations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40072-024-00328-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们介绍了通过随机量子化（SQ）建立欧氏量子场论（EQFTs）相关函数指数衰减的两种方法。特别是，我们考虑了霍恩-克罗恩（或 \(\exp (\α \phi )_2\)) 的椭圆随机量子化。EQFT in two dimensions.第一种方法基于路径耦合论证和 PDE 先验估计，第二种方法基于 SQ 方程解的马利亚文导数估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.