##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Michael Anshelevich

#### Texas A&M

## The exponential homomorphism in non-commutative probability

##### Abstract:

The wrapping transformation is easily seen to intertwine convolutions of probability measures on the real line and the circle. It is also easily seen to not transform additive free convolution into the multiplicative one. However, we show that on a large class L of probability measures on the line, wrapping does transform not only the free but also Boolean and monotone convolutions into their multiplicative counterparts on the circle. This allows us to prove various identities between multiplicative convolutions by simple applications of the additive ones. The restriction of the wrapping to L has several other unexpected nice properties, for example preserving the number of atoms. This is joint work with Octavio Arizmendi.

Host: Todd Kemp

### February 4, 2016

### 9:00 AM

### AP&M 6402

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