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A.s. convergence for infinite colour Pólya urns associated with random walks

Svante Janson Department of Mathematics, Uppsala University, Uppsala, Sweden

Probability mathscidoc:2203.28001

Arkiv for Matematik, 59, (1), 87-123, 2020.5
We consider Pólya urns with infinitely many colours that are of a random walk type, in two related versions. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014–2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence assuming exponential moment).
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@inproceedings{svante2020a.s.,
  title={A.s. convergence for infinite colour Pólya urns associated with random walks},
  author={Svante Janson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311103441830354954},
  booktitle={Arkiv for Matematik},
  volume={59},
  number={1},
  pages={87-123},
  year={2020},
}
Svante Janson. A.s. convergence for infinite colour Pólya urns associated with random walks. 2020. Vol. 59. In Arkiv for Matematik. pp.87-123. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311103441830354954.
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