Algebraic approach to the interacting particle systems theory
Interacting particle systems are mathematical models consisting of many interacting units which evolve stochastically. They were introduced to model diffusion of particles in gases and liquids, the evolution of traits in a population, the spread of viruses, the dynamics of opinions, and various other systems in the natural and social sciences. Many interesting phenomena such as phase transitions, metastability, random interfaces, are well described by interacting particle systems. Some of them, such as the asymmetric exclusion process, became paradigmatic in non-equilibrium statistical physics.
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