The sample paths of L/'evy processes generate various random fractals and many of their properties have been studied since 1960's [see the survey papers of Fristedt (1974), Taylor (1986) and Xiao (2004)].
In this talk we present some recent results on potential theory of multiparameter L/'evy processes and show their applications to Hausdorff dimension and exact capacity computation for ordinary L/'evy processes. In particular, we verify a conjecture of Bertoin (1997, 1999) on intersections of independent regenerative sets and derive some intersection properties of operator-stable L/'evy processes.
This talk is based on joint works with D. Khoshnevisan.