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Waves and particles in random media with slowly decaying correlationsMathematical Physics & Probability
|Speaker: ||Lenya Ryzhik, University of Chicago|
|Location: ||2112 MSB|
|Start time: ||Wed, Apr 22 2009, 4:10PM|
Weakly random media affect propagation of waves and particles over
long distances in a non-trivial way. When medium correlations decay rapidly
the long time behavior is reasonably well understood: both waves and
particles behave, loosely speaking, diffusively, and most non-trivial
phenomena happen on the same time scale. Slow decay of media correlations
seems to produce an interesting effect when single particle behavior becomes
non-trivial on a much shorter time scale than the multi-particle behavior.
Similarly, the wave phase becomes random long before wave energy randomizes.
Moreover, while some quantities acquire fractional Brownian
limits because of the slow correlations decay, others keep their diffusive
limits. I will describe some rigorous as well as formal results in these
directions. This is a joint work in progress with T.Komorowski.