LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION

Hao Shen; Scott A. Smith; Rongchan Zhu; Xiangchan Zhu

doi:10.1214/21-AOP1531

LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION

Hao Shen
, Scott A. Smith^*
, Rongchan Zhu
, Xiangchan Zhu

^*此作品的通讯作者

数学学院

University of Wisconsin
Chinese Academy of Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

17 引用（Scopus）

摘要

This article studies large N limits of a coupled system of N interacting Φ⁴ equations posed over T^d for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order 1/ √ N with respect to the Wasserstein distance.

源语言	英语
页（从-至）	131-202
页数	72
期刊	Annals of Probability
卷	50
期	1
DOI	https://doi.org/10.1214/21-AOP1531
出版状态	已出版 - 1月 2022

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@article{996eabe9921746e8b02960a5ce31fc41,

title = "LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION",

abstract = "This article studies large N limits of a coupled system of N interacting Φ4 equations posed over Td for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order 1/ √ N with respect to the Wasserstein distance.",

keywords = "Mean-field limit, O(n) linear sigma model, Space-time white noise, Stochastic quantization, Φ",

author = "Hao Shen and Smith, \{Scott A.\} and Rongchan Zhu and Xiangchan Zhu",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022",

year = "2022",

month = jan,

doi = "10.1214/21-AOP1531",

language = "English",

volume = "50",

pages = "131--202",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

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TY - JOUR

T1 - LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION

AU - Shen, Hao

AU - Smith, Scott A.

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2022

PY - 2022/1

Y1 - 2022/1

N2 - This article studies large N limits of a coupled system of N interacting Φ4 equations posed over Td for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order 1/ √ N with respect to the Wasserstein distance.

AB - This article studies large N limits of a coupled system of N interacting Φ4 equations posed over Td for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order 1/ √ N with respect to the Wasserstein distance.

KW - Mean-field limit

KW - O(n) linear sigma model

KW - Space-time white noise

KW - Stochastic quantization

KW - Φ

UR - https://www.scopus.com/pages/publications/85125703387

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DO - 10.1214/21-AOP1531

M3 - Article

AN - SCOPUS:85125703387

SN - 0091-1798

VL - 50

SP - 131

EP - 202

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION

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