##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Lei Wu

#### UCSD Graduate Student

## Random inscribing polytopes

##### Abstract:

Given a fixed convex body $K$, choose $n$ points randomly on the boundary of $K$ according to a ``uniform" distribution, and call the convex hull of these $n$ points a Random Inscribing Polytope. We will discuss some recent asymptotic results on the volume of these polytopes. Namely, we will prove a lower bound on the variance, some concentration result, and an analogue of the central limit theorem. This is joint work with Ross Richardson and Van Vu.

Host:

### May 17, 2005

### 4:00 PM

### AP&M 7321

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