Diffusion in large networks

We investigate the phenomenon of diffusion in a countably infinite society individuals interacting with their neighbors network. At given time, each individual is either active or inactive. The driven by two characteristics: network structure and mechanism represented an aggregation function. distinguish between mechanisms (probabilistic, deterministic) focus on types functions (strict, Boolean). Under strict functions, polarization cannot happen, its state evolves towards mixture infinitely many inactive agents, homogeneous society. Boolean process becomes deterministic contagion model Morris (2000) particular case our framework. Polarization can then happen. Our dynamics also allows for cycles both cases. not relevant these questions, but important establishing irreducibility, at price richness assumption: should contain least one complex star have enough space storing local configurations. be game-theoretic interpretation via coordination game, where player would apply best-response strategy random neighborhood.