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

doi:10.1214/21-AOP1531

CSpace > 应用数学研究所

	LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION
	Shen, Hao 1; Smith, Scott A.2 ; Zhu, Rongchan 3; Zhu, Xiangchan2
	2022
发表期刊	ANNALS OF PROBABILITY
ISSN	0091-1798
卷号	50 期号:1 页码:131-202
摘要	This article studies large N limits of a coupled system of N interacting Phi(4) 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/root N with respect to the Wasserstein distance. We also consider fluctuations and obtain tightness results for certain O(N) invariant observables, along with an exact description of the limiting correlations.
关键词	O(N) linear sigma model Phi(4) mean-field limit stochastic quantization space-time white noise
DOI	10.1214/21-AOP1531
收录类别	SCI
语种	英语
资助项目	NSF[DMS-1712684/DMS-1909525] ; NSF[DMS-1954091] ; NSFC[11922103] ; NSFC[11771037] ; NSFC[12090014] ; NSFC[11688101] ; National Key R&D Program of China[2020YFA0712700] ; key Lab of Random Complex Structures and Data Science, Youth Innovation Promotion Association, Chinese Academy of Science[2020003] ; DFG[CRC 1283]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000760718500005
出版者	INST MATHEMATICAL STATISTICS-IMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60092
专题	应用数学研究所
通讯作者	Smith, Scott A.
作者单位	1.Univ Wisconsin, Dept Math, Madison, WI 53706 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Beijing Inst Technol, Dept Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Shen, Hao,Smith, Scott A.,Zhu, Rongchan,et al. LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION[J]. ANNALS OF PROBABILITY,2022,50(1):131-202.
APA	Shen, Hao,Smith, Scott A.,Zhu, Rongchan,&Zhu, Xiangchan.(2022).LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION.ANNALS OF PROBABILITY,50(1),131-202.
MLA	Shen, Hao,et al."LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION".ANNALS OF PROBABILITY 50.1(2022):131-202.