Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Nonlinear Dynamics, Synchronization and Chaos

DY 31.12: Talk

Wednesday, April 3, 2019, 13:00–13:15, H20

Field-theoretic approach to the universality of branching processes — •Johannes Pausch, Rosalba Garcia-Millan, Benjamin Walter, and Gunnar Pruessner — Department of Mathematics, Imperial College London, UK

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 characterise 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.