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

文献类型：期刊论文

作者Shen, Hao3; Smith, Scott A.2; Zhu, Rongchan1; Zhu, Xiangchan2
刊名ANNALS OF PROBABILITY
出版日期2022
卷号50期号:1页码:131-202
关键词O(N) linear sigma model Phi(4) mean-field limit stochastic quantization space-time white noise
ISSN号0091-1798
DOI10.1214/21-AOP1531
英文摘要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.
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
语种英语
WOS记录号WOS:000760718500005
出版者INST MATHEMATICAL STATISTICS-IMS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60091]  
专题应用数学研究所
通讯作者Smith, Scott A.
作者单位1.Beijing Inst Technol, Dept Math, Beijing, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
3.Univ Wisconsin, Dept Math, Madison, WI 53706 USA
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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