Abstract.
In this paper we derive formulae for the eigenvalues and spectral gap of the master equation for general collision kernels. We prove a conjecture of Mark Kac's on the existence of a spectral gap independent of the number of particles. We relate the eigenvalues to the “nonlinear” eigenvalues that occur in the exact solutions of model Boltzmann equations due to M. Ernst.
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Received: 30 November 2001; in final form: 26 March 2002/Published online: 2 December 2002
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Maslen, D. The eigenvalues of Kac's master equation. Math Z 243, 291–331 (2003). https://doi.org/10.1007/s00209-002-0466-y
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DOI: https://doi.org/10.1007/s00209-002-0466-y