We start with showing how rearrangement inequalities may be used in probabilistic contexts such as e.g. for obtaining bounds on survival probabilities in trapping models. This naturally motivates the need for a new rearrangement inequality which can be interpreted as involving symmetric rearrangements around infinity. After outlining the proof of this inequality we proceed to give some further applications to the volume of Lévy sausages as well as to capacities for Lévy processes.
(Joint work with P. Sousi and R. Sun)