  We prove a new rearrangement inequality for multiple integrals, which partly
generalizes a result of Friedberg and Luttinger (1976) and can be interpreted
as involving symmetric rearrangements of domains around infinity. As
applications, we prove two comparison results for general Levy processes and
their symmetric rearrangements. The first application concerns the survival
probability of a point particle in a Poisson field of moving traps following
independent Levy motions. We show that the survival probability can only
increase if the point particle does not move, and the traps and the Levy
motions are symmetrically rearranged. This essentially generalizes an
isoperimetric inequality of Peres and Sousi (2011) for the Wiener sausage. In
the second application, we show that the q-capacity of a Borel measurable set
for a Levy process can only decrease if the set and the Levy process are
symmetrically rearranged. This result generalizes an inequality obtained by
Watanabe (1983) for symmetric Levy processes.
