Bounds for the state-modulated resolvent of a linear Boltzmann generator
Mathematical Physics
2015-05-30 v1 math.MP
Probability
Abstract
We study a generalized resolvent for the generator of a Markovian semigroup. The Markovian generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential and colliding elastically with particles from an ideal background gas. We obtain bounds for the state-modulated resolvent which are relevant in the regime where the mass ratio between the test particle and a particle from the gas is large. These bounds relate to the typical amount of time that the particle spends in different regions of phase space before arriving to a region around the origin.
Keywords
Cite
@article{arxiv.1110.0689,
title = {Bounds for the state-modulated resolvent of a linear Boltzmann generator},
author = {Jeremy Clark and Loïc Dubois},
journal= {arXiv preprint arXiv:1110.0689},
year = {2015}
}
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31 pages