Random Homeomorphisms in Analysis
Peter Jones
Yale University
Mathematics
Random homeomorphisms appear in several natural problems in analysis, for exampl
e SLE, a process introduced by Oded Schramm. These mappings necessarily have mul
tiscale descriptions. We will discuss some spaces of homeomorphisms along with t
heir geometric realization as "welding curves" and quasiconformal mappings. Thes
e constructions are also linked to certain problems on complex analysis, singula
r integrals, and square functions, and are analyzed by combining methods from ha
rmonic analysis and probability theory.