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In 1956, Mark Kac proposed a novel
approach to the study of the
Boltzmann equation via the large N limit of a stochastic system of N
particle undergoing binary collisions. In the 1960's, Henry McKean and
his students made many significant contributions to this program,
particularly with regard to the problem of propagation of chaos. However,
analysis of the rate of equilibriation for this
model remained an open problem for many years, and progress on this front was
much more recent. Until now, this
progress has been made for what corresponds to "Maxwellian
molecules". Recent work of myself, Carvalho and Loss
extends this progress to the physically significant hard-sphere case. The colloquium will at least explain this
progress, but shall assume nothing in the way of familiarity with Kac's program, or even the Boltzmann equation: It will be
aimed at a general mathematical audience.
http://www.math.rutgers.edu/~carlen/
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