##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability and Statistics Seminar

## Masha Gordina

#### University of Connecticut

## Gaussian type measures on infinite-dimensional Heisenberg groups

##### Abstract:

The groups in question are modeled on an abstract Wiener space. Then a group Brownian motion is defined, and its properties are studied in connection with the geometry of this group. The main results include quasi-invariance of the Gaussian (heat kernel) measure, log Sobolev inequality (following a bound on the Ricci curvature), and the Taylor isomorphism to the corresponding Fock space. The latter map is a version of the Ito-Wiener expansion in the non-commutative setting. This is a joint work with B. Driver.

Host: Bruce Driver

### May 14, 2009

### 10:00 AM

### AP&M 6402

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