Universal cover-time distribution of heterogeneous random walks

doi:10.1103/PhysRevE.107.024128

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	Universal cover-time distribution of heterogeneous random walks
	Dong, Jia-Qi ; Han, Wen-Hui ; Wang, Yisen ; Chen, Xiao-Song ; Huang, Liang 3,3
刊名	PHYSICAL REVIEW E
	2023
卷号	107 期号:2 页码:24128
关键词	SYSTEMS
ISSN号	2470-0045
DOI	10.1103/PhysRevE.107.024128
英文摘要	The cover-time problem, i.e., the time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk on complex structures has been a long-standing challenge and has attracted persistent efforts. Usually it is assumed that the random walk is noncompact, to facilitate theoretical treatments by neglecting the correlations between visits. The known results are essentially limited to noncompact and homogeneous systems, where different sites are on an equal footing and have identical or close mean first-passage times, such as random walks on a torus. In contrast, realistic random walks are prevailingly heterogeneous with diversified mean first-passage times. Does a universal distribution still exist? Here, by considering the most general situations of noncompact random walks, we uncover a generalized rescaling relation for the cover time, exploiting the diversified mean first-passage times that have not been accounted for before. This allows us to concretely establish a universal distribution of the rescaled cover times for heterogeneous noncompact random walks, which turns out to be the Gumbel universality class that is ubiquitous for a large family of extreme value statistics. Our analysis is based on the transfer matrix framework, which is generic in that, besides heterogeneity, it is also robust against biased protocols, directed links, and self-connecting loops. The finding is corroborated with extensive numerical simulations of diverse heterogeneous noncompact random walks on both model and realistic topological structures. Our technical ingredient may be exploited for other extreme value or ergodicity problems with nonidentical distributions.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/28103]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	1.[Dong, Jia-Qi 2.Han, Wen-Hui 3.Wang, Yisen 4.Lanzhou Univ, Key Lab Theoret Phys Gansu Prov, Lanzhou 730000, Gansu, Peoples R China 5.Lanzhou Univ, Lanzhou Ctr Theoret Phys, Lanzhou 730000, Gansu, Peoples R China 6.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 7.Beijing Normal Univ, Sch Syst Sci, Beijing 100875, Peoples R China
推荐引用方式 GB/T 7714	Dong, Jia-Qi,Han, Wen-Hui,Wang, Yisen,et al. Universal cover-time distribution of heterogeneous random walks[J]. PHYSICAL REVIEW E,2023,107(2):24128.
APA	Dong, Jia-Qi,Han, Wen-Hui,Wang, Yisen,Chen, Xiao-Song,&Huang, Liang.(2023).Universal cover-time distribution of heterogeneous random walks.PHYSICAL REVIEW E,107(2),24128.
MLA	Dong, Jia-Qi,et al."Universal cover-time distribution of heterogeneous random walks".PHYSICAL REVIEW E 107.2(2023):24128.