Symmetrization Resistance in Random Variables and Entropy
Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore a 53-minute mathematics lecture from the Hausdorff Center for Mathematics examining the concept of symmetrization resistance in asymmetric random variables. Delve into how an asymmetric random variable X demonstrates symmetrization resistance when any independent random variable Y creating a symmetric sum X+Y must have greater variance than X. Learn about the groundbreaking work by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999) on asymmetric Bernoulli random variables, and Pal's (2008) stochastic calculus proof. Discover the novel concept of entropic symmetrization resistance, where entropy replaces variance as the key measure, and understand how Bernoulli random variables exhibit both traditional and entropic symmetrization resistance under the same conditions. Examine the extension of entropy and variance inequalities to the hypercube and investigate potential applications to non-Bernoulli random variables, featuring collaborative research with Mokshay Madiman.