Limit of 1-Dimensional Mixed-Mechanism Interacting Particle System Model

2018/12/08 by Zhao, Tong
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.04938

Abstract

Elaborating on the model from voter process with mixed-mechanism under suitable scaling, I have two new mechanisms which are random switch and unbiased local Homogenization and subtly biased advantage but with state dependent coefficient involved. The most crucial one, the existence of high-frequency duplication generating the diffusion term and noise term in each case identifies the limit equation as SPDE driven by space time white noise.

Related

• Voter Model Perturbations and Reaction Diffusion Equations
• Equilibrium interfaces of biased voter models
• The noisy voter-exclusion process
• Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises
• Thermodynamic Limit of Interacting Particle Systems over Time-varying Sparse Random Networks