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DOI:	10.1371/journal.pone.0161586
论文题名:	Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process
作者:	Álvaro Corral; Rosalba Garcia-Millan; Francesc Font-Clos
刊名:	PLOS ONE
ISSN:	1932-6203
出版年:	2016
发表日期:	2016-9-1
卷:	11, 期:9
语种:	英语
英文关键词:	Random walk ; Probability distribution ; Generating functions ; Thermodynamics ; Statistical theories ; Magnetic fields ; Isotherms ; Statistical mechanics
英文摘要:	The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary.
URL:	http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0161586&type=printable
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资源类型:	期刊论文
标识符:	http://119.78.100.158/handle/2HF3EXSE/25552
Appears in Collections:	过去全球变化的重建影响、适应和脆弱性科学计划与规划气候变化与战略全球变化的国际研究计划气候减缓与适应气候变化事实与影响

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journal.pone.0161586.PDF（652KB）	期刊论文	作者接受稿	开放获取	CC BY-NC-SA	View Download

作者单位:

Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain;Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain;London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom;Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, United Kingdom;ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy

Recommended Citation:

Álvaro Corral,Rosalba Garcia-Millan,Francesc Font-Clos. Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process[J]. PLOS ONE,2016-01-01,11(9)

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