The diffusion of opposite opinions in a randomly biased environment

Abstract

We propose a model for diffusion of two opposite opinions in which the decision to be taken by each individual is a random variable depending on the tendency of the population, as well on its own trend characteristic. The influence of the population can be positive, negative or non-existent in a random form. We prove a phase transition in the behaviour of the proportion of each opinion, such that, the mean square proportions are linear functions of time in the diffusive case, but are given by a power law in the superdiffusive regime.

Reinforced random walks under memory lapses

“…This refers to the fact that the second moment of the position is scaled linearly (diffusive) or as a power law (super-diffusive). This fact has motivated the development of new models and results that generalize the ERW, for instance, Bercu and Laulin [4,5], Bertoin [7,8,9], González-Navarrete and Lambert [13,15] and Gut and Stadtmüller [16,17].…”