Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics

Abstract

We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter $p$ which drives an order disorder transition at a critical value $p_c$. The distribution $S(X,t)$ of the displacements $X$ from the origin of the walkers is computed at different times. Below $p_c$, two time scales associated with a crossover behavior in time are detected, which diverge in a power law manner at criticality with different exponent values. $S(X,t)$ also carries the signature of the phase transition as it changes its form at $p_c$. The walks show the features of a biased random walk below $p_c$, and above $p_c$, the walks are like unbiased random walks. The bias vanishes in a power law manner at $p_c$ and the width of the resulting Gaussian function shows a discontinuity. Some of the features of the walks are argued to be comparable to the critical quantities associated with the mean field Ising model, to which class the opinion dynamics model belongs. The results for the Markovian and non-Markovian walks are almost identical which is justified by considering the different fluxes. We compare the present results with some earlier similar studies.

References in corpus (20)

• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Disorder induced phase transition in kinetic models of opinion dynamics
• Opinion formation in the kinetic exchange models: Spontaneous symmetry breaking transition
• Large deviations and nontrivial exponents in coarsening systems
• Diffusive persistence and the `sign-time' distribution
• Mean field solutions of kinetic exchange opinion models
• Generalized persistence exponents: an exactly soluble model
• Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions
• Phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges
• Persistence in the Voter model: continuum reaction-diffusion approach
• Three-state opinion dynamics in modular networks
• Stationary definition of persistence for finite temperature phase ordering
• Symmetry breaking by heating in a continuous opinion model
• Long route to consensus: Two stage coarsening in a binary choice voting model
• Agent dynamics in kinetic models of wealth exchange
• Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature
• Opinion dynamics model with domain size dependent dynamics: novel features and new universality class
• Antipersistent dynamics in kinetic models of wealth exchange
• Virtual walks in spin space: a study in a family of two-parameter models
• Tagged particle dynamics in one dimensional $A+A\to kA$ models with the particles biased to diffuse towards their nearest neighbour

Cited by in corpus (2)

• Virtual walks and phase transitions in two dimensional BChS model with extreme switches
• Random walk with multiple memory channels: a new paradigm