Anomalous finite-size scaling in higher-order processes with absorbing states

Abstract

We study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory (also referred to as Wentzel-Kramers-Brillouin (WKB) method in some contexts). We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites, as a function of parameters and network size $N$. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the $q$-susceptible-infected-susceptible ($q-SIS$) model, i.e., a high-order epidemic model requiring of $q$ active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with non-trivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for $[1\le q\le 3]$, with a maximal variability at $q=2$, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability and that the leading-order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states.

10 pages, 4 figures

References in corpus (10)

• Statistical physics of social dynamics
• The large deviation approach to statistical mechanics
• The physics of higher-order interactions in complex systems
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Complex contagion process in spreading of online innovation
• Langevin description of critical phenomena with two symmetric absorbing states
• The spectral dimension of simplicial complexes: a renormalization group theory
• Universality, criticality and complexity of information propagation in social media
• Sideward contact tracing and the control of epidemics in large gatherings
• Simplicial temporal networks from Wi-Fi data in a University Campus: the effects of restrictions on epidemic spreading