Abstract: It is a well-known, yet striking, phenomenon in various fields of mathematics that sometimes a random selection can produce a better outcome than any explicit choice known to us. I will discuss a couple of recent examples of this probabilistic method that have played an important role in questions of mathematical analysis:
- a random decomposition of non-homogeneous singular integrals by F. Nazarov, S. Treil and A. Volberg, and
- a probabilistic construction of interpolating spline functions in very general domains by P. Auscher and myself.
