Interacting particle systems (IPS) are mathematical models used to describe the dynamics of a collection of particles that interact with one another according to certain rules. These systems are commonly studied in statistical physics, probability theory, and various fields of applied mathematics due to their ability to model complex phenomena in nature, such as the behavior of gases, biological systems, and social dynamics.
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An interacting particle system is a stochastic process whose local states evolve through random transitions whose rates depend on nearby states.