@misc{10481/80035,
year = {2023},
month = {1},
url = {https://hdl.handle.net/10481/80035},
abstract = {Here we study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory [also referred to as the 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 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 nontrivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for [1≤q≤3], with a maximal variability at q=2, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability. Moreover, 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. Some possible extensions of this work are also discussed.},
organization = {Spanish Ministry and Agencia Estatal de Investigación (AEI) through Project of I+D+i, Ref. No. PID2020-113681GB-I00, financed by Grant No. MICIN/AEI/10.13039/501100011033},
organization = {FEDER “A way
to make Europe,” as well as the Consejería de Conocimiento,
Investigación Universidad, Junta de Andalucía and European
Regional Development Fund, project Ref. No. P20-00173},
publisher = {American Physical Society},
title = {Anomalous finite-size scaling in higher-order processes with absorbing states},
doi = {10.1103/PhysRevE.107.014105},
author = {Vezzani, Alessandro and Muñoz Martínez, Miguel Ángel and Burioni, Raffaella},
}