Critical properties of the susceptible-exposed-infected model with correlated temporal disorder.

In this paper we study the critical properties of the nonequilibrium phase transition of the susceptible-exposed-infected (SEI) model under the effects of long-range correlated time-varying environmental noise on the Bethe lattice. We show that temporal noise is perturbatively relevant changing the universality class from the (mean-field) dynamical percolation to the exotic infinite-noise universality class of the contact process model. Our analytical results are based on a mapping to the one-dimensional fractional Brownian motion with an absorbing wall and is confirmed by Monte Carlo simulations.

Extinction transitions in correlated external noise.

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e.

Fractional Brownian motion with a reflecting wall.

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior 〈x^{2}〉∼t^{α}, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier.