16 citations · 36 across the 6 of their papers we have counts for
6 papers
A Nonlinear Transform for the Diagonalization of the Bernoulli-Laplace Diffusion Model and Orthogonal Polynomials
Chjan Lim, William Pickering
The Bernoulli-Laplace model describes a diffusion process of two types of particles between two urns. To analyze the finite-size dynamics of this process, and for other constructiv…
Analysis of the high dimensional naming game with committed minorities
William Pickering, Boleslaw K. Szymanski, Chjan Lim
The naming game has become an archetype for linguistic evolution and mathematical social behavioral analysis. In the model presented here, there are individuals and words.…
Solution of the multi-state voter model and application to strong neutrals in the naming game
William Pickering, Chjan Lim
We consider the voter model with states initially in the system. Using generating functions, we pose the spectral problem for the Markov transition matrix and solve for all eig…
Spectral solution of urn models for interacting particle systems
William Pickering, Chjan Lim
Using generating function methods for diagonalizing the transition matrix in 2-Urn models, we provide a complete classification into solvable and unsolvable subclasses, with furthe…
Information Sharing for Strong Neutrals on Social Networks - Exact Solutions for Consensus Times
Chjan Lim, William Pickering
To analyze the nuances of the root concept of neutral in social networks, we focus on several related interpretations and suggest corresponding mathematical models for each of them…
Solution of the Voter Model by Spectral Analysis
William Pickering, Chjan Lim
An exact spectral analysis of the Markov Propagator for the Voter model is presented for the complete graph, and extended to the complete bipartite graph and uncorrelated random ne…