Dirichlet forms and polymer models based on stable processes

doi:10.1016/j.spa.2020.04.011

CSpace > 应用数学研究所

	Dirichlet forms and polymer models based on stable processes
	Li, Liping1 ; Li, Xiaodan 2
	2020-10-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	130 期号:10 页码:5940-5972
摘要	In this paper, we are concerned with polymer models based on a-stable processes, where alpha is an element of (d/2, d (<^>) 2) and d stands for dimension. They are attached with a delta potential at the origin and the associated Gibbs measures are parametrized by a constant gamma is an element of R boolean OR {-infinity} playing the role of inverse temperature. Phase transition exhibits with critical value gamma(cr) = 0. Our first object is to formulate the associated Dirichlet form of the canonical Markov process X-(gamma) induced by the Gibbs measure for a globular state gamma > 0 or the critical state gamma = 0. Approach of Dirichlet forms also leads to deeper descriptions of their probabilistic counterparts. Furthermore, we will characterize the behaviour of polymer near the critical point from probabilistic viewpoint by showing that X-(gamma) is convergent to X-(0) as gamma down arrow 0 in a certain meaning. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Dirichlet forms Polymer models Self-adjoint extensions Stable processes
DOI	10.1016/j.spa.2020.04.011
收录类别	SCI
语种	英语
资助项目	NSFC, China[11871162] ; Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000562734000003
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52019
专题	应用数学研究所
通讯作者	Li, Xiaodan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, RCSDS, Beijing 100190, Peoples R China 2.Fudan Univ, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Li, Liping,Li, Xiaodan. Dirichlet forms and polymer models based on stable processes[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2020,130(10):5940-5972.
APA	Li, Liping,&Li, Xiaodan.(2020).Dirichlet forms and polymer models based on stable processes.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,130(10),5940-5972.
MLA	Li, Liping,et al."Dirichlet forms and polymer models based on stable processes".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.10(2020):5940-5972.