Persistence in the Voter model: continuum reaction-diffusion approach

Abstract

We investigate the persistence probability in the Voter model for dimensions d\geq 2. This is achieved by mapping the Voter model onto a continuum reaction-diffusion system. Using path integral methods, we compute the persistence probability r(q,t), where q is the number of ``opinions'' in the original Voter model. We find r(q,t)\sim exp[-f_2(q)(ln t)^2] in d=2; r(q,t)\sim exp[-f_d(q)t^{(d-2)/2}] for 2<d<4; r(q,t)\sim exp[-f_4(q)t/ln t] in d=4; and r(q,t)\sim exp[-f_d(q)t] for d>4. The results of our analysis are checked by Monte Carlo simulations.

arXiv comment10 pages, 3 figures, Latex, submitted to J. Phys. A (letters)

References in corpus (6)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Coarsening and persistence in the voter model
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Proportion of Unaffected Sites in a Reaction-Diffusion Process
• Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

Cited by in corpus (23)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• The Naming Game in Social Networks: Community Formation and Consensus Engineering
• Large deviations and nontrivial exponents in coarsening systems
• Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models
• Reaction Diffusion Models in One Dimension with Disorder
• Numerical study of persistence in systems with absorbing states
• Analytical results for random walk persistence
• Boundary effects in a three-state modified voter model for languages
• Local Persistence in the Directed Percolation Universality Class
• Percolation and coarsening in the bidimensional voter model
• Analytical Study of Giant Fluctuations and Temporal Intermittency in an Aggregation Model
• Persistence in Cluster--Cluster Aggregation
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Finite-size effects on the convergence time in continuous-opinion dynamics
• Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics
• The Concealed Voter Model is in the Voter Model universality class
• Virtual walks in spin space: a study in a family of two-parameter models
• Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model
• Voter Dynamics on an Ising Ladder: Coarsening and Persistence
• Generating Function for Particle-Number Probability Distribution in Directed Percolation
• Diffusive Persistence on Disordered Lattices and Random Networks
• Fluctuations and Persistence in Quantum Diffusion on Regular Lattices