Thomas Chen
L^r-Convergence of 
a Random Schr\"odinger to a Linear 
Boltzmann Evolution
(147K, AMS Latex)

ABSTRACT.  We study the macroscopic scaling and weak coupling 
limit for a random Schr\"odinger 
equation on $\Z^3$. 
We prove that the Wigner transforms of a large class 
of "macroscopic" solutions converge in 
$r$-th mean to solutions of a linear Boltzmann equation, 
for any finite value of $r\in\R_+$. 
This extends previous 
results where convergence in expectation was established.