Noisy voter model: Explicit expressions for finite system size

FLORENCIA PERACHIA; ROMÁN, PABLO; MENCHÓN, SILVIA ADRIANA

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Año: 2022 vol. 106

1063-651X

Urn models are classic stochastic models that have been used to describe a diverse kind of complex systems. Voter and Ehrenfest´s models are very well known urn models. An opinion model that combines these two models is presented in this work, and it is used to study a noisy voter model. In particular, at each temporal step, an Ehrenfest´s model step is done with probability $alpha$ or a voter step is done with probability $1-alpha$. The parameter $alpha$ plays the role of a noise. By performing a spectral analysis, it is possible to obtain explicit expressions for the order parameter, susceptibility and Binder´s fourth-order cumulant. Recursive expressions in terms of the Dual Hahn polynomials are given for first passage and return distributions to consensus and equal coexistence of opinions. In the cases where they follow power-law distributions, their exponents are computed. This model has a pseudo-critical noise value that depends on the system size, a discussion about thermodynamic limits is given.