Fractional Response and Parameter Almost Sure Invariance Principle for the Quadratic Family

Explore a 52-minute conference talk from the Workshop on "Rare Events in Dynamical Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into an almost sure invariance principle in parameter space for the quadratic family, inspired by Daniel Schnellmann's work on piecewise expanding systems. Discover how this principle implies statistical properties like the central limit theorem and the law of the iterated logarithm. Learn about the normal distribution of ergodic averages as a function of parameter in the quadratic family after appropriate scalings. Consider potential applications to fractional response, drawing from Amanda de Lima and Daniel Smania's research. Gain insights into advanced mathematical concepts and their implications in dynamical systems theory.