Field-theoretic approach to the universality of branching processes

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Title: Field-theoretic approach to the universality of branching processes
Authors: Garcia Millan, R
Pausch, J
Walter, B
Pruessner, G
Item Type: Journal Article
Abstract: Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the n-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.
Issue Date: 6-Dec-2018
Date of Acceptance: 9-Nov-2018
ISSN: 1539-3755
Publisher: American Physical Society
Journal / Book Title: Physical Review E
Volume: 98
Copyright Statement: ©2018 American Physical Society
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Publication Status: Published
Article Number: 062107
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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