Matija Vidmar

Stability and sensitivity of random variables, d'après Tsirelson

Tsirelson introduced the notion of a noise-type Boolean algebra, modeled on the properties of the family of sigma-fields of a stochastic noise. We recall these and some accompanying notions, and reveal that the stable sigma-field of a noise-type Boolean algebra, as generated by the so-called stable random variables, belongs to its topological/monotone closure. As an application we consider another kind of stability/sensitivity property (distinct from the aforementioned one) of the time of maximum of Brownian motion on a compact interval that displays some difficult-to-intuit and perhaps unexpected behavior. (Joint work with Jon Warren.)