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A cluster expansion approach to a one-dimensional Boltzmann equation: A validity result. (English) Zbl 0811.60099

Summary: We consider a stochastic particle system on the line and prove that, when the number of particles diverges and the probability of a collision is suitably rescaled, the system is well described by a one-dimensional Boltzmann equation. The result holds globally in time, without any smallness assumption.

MSC:

60K40 Other physical applications of random processes
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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