Many statistical sampling problems come with inherent biases, which can be (partly) reversed with different bias transforms, usually requiring non-zero mean. For distributions with mean 0, a limit case called the zero bias was introduced by Goldstein and Reinert in 1997. The zero bias has strong connections to Stein's method, offers powerful tools for quantitative normal approximation, and has recently discovered intriguing applications to infinite divisibility.

In this talk, I will report on ongoing work with Larry Goldstein on an analog of the zero bias transform in free probability. I will discuss existence and smoothing properties, using Cauchy transform and subordination methods, and connection to free Stein kernels. I will then present our main theorem, characterizing free infinite divisibility in terms of the zero bias, and providing a concrete meaning to the free Levy-Khinchine measure for such distributions.

Bio: Todd Kemp is a Canadian/American mathematician, whose research interests include random matrix theory, free probability, stochastic analysis, coercive functional inequalities, and harmonic analysis. Earning his PhD at Cornell University in 2005, he was a CLE Moore Instructor at MIT before joining the faculty at UC San Diego in 2009, where he is Professor and Vice Chair for Graduate Affairs.