Probability Seminars

## Limits of Polya urns with innovations

### With Jean Bertoin (Zurich)

# Limits of Polya urns with innovations

We consider a version of the classical P’olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set.

After each sampling of a ball in the urn, one returns $C$ balls of the same color and additional balls of different colors given by some finite point process $xi$ on $S$.

When the number of steps goes to infinity, the empirical distribution of the colors in the urn converges to the normalized intensity measure of $xi$, and we analyze the fluctuations.

The ratio $rho= E©/E®$ of the average number of copies to the average total number of balls returned plays a key role.

- Speaker: Jean Bertoin (Zurich)
- Wednesday 07 September 2022, 09:00–10:00
- Venue: MR9, Centre for Mathematical Sciences.
- Series: Probability; organiser: Jason Miller.