Exact derivation of a finite-size scaling law and corrections to scaling in the geometric galton-watson process

Title: Exact derivation of a finite-size scaling law and corrections to scaling in the geometric galton-watson process
Authors: Corral, A
Garcia-Millan, R
Font-Clos, F
Item Type: Journal Article
Abstract: 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.
Issue Date: 1-Sep-2016
Date of Acceptance: 8-Aug-2016
URI: http://hdl.handle.net/10044/1/50405
DOI: https://dx.doi.org/10.1371/journal.pone.0161586
ISSN: 1932-6203
Publisher: Public Library of Science (PLoS)
Start Page: 1
End Page: 17
Journal / Book Title: PLoS ONE
Volume: 11
Issue: 9
Copyright Statement: © 2016 Corral et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Keywords: Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
THERMODYNAMICS
Models, Theoretical
Statistics as Topic
Stochastic Processes
Thermodynamics
Stochastic Processes
Thermodynamics
Models, Theoretical
Statistics as Topic
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
THERMODYNAMICS
MD Multidisciplinary
General Science & Technology
Publication Status: Published
Open Access location: https://doi.org/10.1371/journal.pone.0161586
Article Number: ARTN e0161586
Appears in Collections:Mathematics



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