Spectral gap for Kac's model of Boltzmann equation
Janvresse, Elise
Ann. Probab., Tome 29 (2001) no. 1, p. 288-304 / Harvested from Project Euclid
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We consider a random walk on $S^{n-1}$ , the standard sphere of dimension $n -1$, generated by random rotations on randomly selected coordinate planes $i,j$ with $1 \le i < j \le n$. This dynamic was used by Marc Kac as a model for the spatially homogeneous Boltzmann equation. We prove that the spectral gap on $S^{n-1}$ is $n^{-1}$ up to a constant independent of $n$.
Publié le : 2001-02-14
Classification:  Spectral gap,  Kac’s model,  Boltzmann equation,  60K35 
@article{1008956330,
     author = {Janvresse, Elise},
     title = {Spectral gap for Kac's model of Boltzmann equation},
     journal = {Ann. Probab.},
     volume = {29},
     number = {1},
     year = {2001},
     pages = { 288-304},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1008956330}
}

Janvresse, Elise. Spectral gap for Kac's model of Boltzmann equation. Ann. Probab., Tome 29 (2001) no. 1, pp.  288-304. http://gdmltest.u-ga.fr/item/1008956330/