KMS Of Academy of mathematics and systems sciences, CAS
LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION | |
Shen, Hao1; Smith, Scott A.2; Zhu, Rongchan3; Zhu, Xiangchan2 | |
2022 | |
Source Publication | ANNALS OF PROBABILITY |
ISSN | 0091-1798 |
Volume | 50Issue:1Pages:131-202 |
Abstract | 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. |
Keyword | O(N) linear sigma model Phi(4) mean-field limit stochastic quantization space-time white noise |
DOI | 10.1214/21-AOP1531 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000760718500005 |
Publisher | INST MATHEMATICAL STATISTICS-IMS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60092 |
Collection | 应用数学研究所 |
Corresponding Author | Smith, Scott A. |
Affiliation | 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 |
Recommended Citation 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. |
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