Multi-drawing Pólya urns via labelled random DAGs
Oberseminar Darmstadt
Datum: 09.07.2026
Zeit: 16:15–17:45 Uhr
- A Pólya urn of replacement matrix $R=(R_{i,j})_{1\leq i,j\leq d}$ is a Markov process that encodes the following experiment: an urn contains balls of $d$ different colours and at every time-step, a ball is drawn uniformly at random in the urn, and if its colour is $i$, then it is replaced in the urn with an additional $R_{i,j}$ balls of colour $j$, for all $1\leq i, j\leq d$. We study a natural extension of this model in which, instead of drawing one ball at each time-step, we draw a set of $m\geq 2$ balls: in this case, the replacement matrix becomes a replacement tensor. Because of the multi-draws, this process can no longer be seen as a branching process, which makes its analysis much more intricate than in the classical Pólya urn case. Partial results proved by martingale and stochastic approximation techniques exist in the literature. We introduce a new approach based on encoding the urn evolution as a stochastic process indexed by a random directed acyclic graph (DAG) and use this approach, together with the theory of stochastic tensors, to prove a convergence theorem for these multi-drawing Pólya urns, with assumptions that are straightforward to check in practice.
Referentin
- Rebecca Steiner, JGU Mainz
Ort
- TU Darmstadt | Raum S2|15 401
- Schlossgartenstraße 7, 64289 Darmstadt
Veranstalter
- Technische Universität Darmstadt
Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde
Kooperationspartner
Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz, Justus-Liebig-Universität Gießen