Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model

Abstract

We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is introduced by considering a position-dependent diffusion coefficient. Exact results for the probability density function and the mean squared displacement are provided. The limiting case of heterogeneous diffusion is analyzed in detail, and the corresponding time-averaged mean-squared displacement is calculated. From the obtained results, an ergodicity breaking is observed.

References in corpus (13)

• Statistical physics of social dynamics
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Exact and explicit probability densities for one-sided Levy stable distributions
• The generalized Cattaneo (telegrapher's) equation and corresponding random walks
• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
• Universal singularities of anomalous diffusion in the Richardson class
• Anomalous diffusion in nonlinear transformations of the noisy voter model
• Integral decomposition for the solutions of the generalized Cattaneo equation
• Influence of external potentials on heterogeneous diffusion processes
• Interplay between particle trapping and heterogeneity in anomalous diffusion
• Anomalous diffusion and long-range memory in the scaled voter model
• Noisy voter model for the anomalous diffusion of parliamentary presence
• Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting