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PreprintarXiv licencearXiv

Asymptotic Behaviour for Isotropic Pearson Random Walks

  • Davide A. Bignamini
  • Emanuele G. Casini
  • Andrea Martinelli
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Abstract

In the Pearson random walk the direction of the i-th step is a random variable uniformly distributed on the d-dimensional sphere, and its length is a non-negative random variable. In a general framework, we are going to study the asymptotic behaviour of the Pearson random walks when the dimension d goes to infinity. Further, we investigate the same convergence result in a more general framework, where both the number and the lengths of the steps depend on the dimension. The results in the present paper can be applied to approximate the distribution of some classical Pearson random walk, for example, in the Dirichlet case.

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Cite

BibTeXRIS
BibTeX
@misc{bignamini2026asymptotic,
  title = {{Asymptotic Behaviour for Isotropic Pearson Random Walks}},
  author = {Davide A. Bignamini and Emanuele G. Casini and Andrea Martinelli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05195},
  eprint = {2609.05195},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05195},
}
RIS
TY  - UNPB
TI  - Asymptotic Behaviour for Isotropic Pearson Random Walks
AU  - Davide A. Bignamini
AU  - Emanuele G. Casini
AU  - Andrea Martinelli
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05195
UR  - https://arxiv.org/abs/2609.05195
AB  - In the Pearson random walk the direction of the i-th step is a random variable uniformly distributed on the d-dimensional sphere, and its length is a non-negative random variable. In a general framework, we are going to study the asymptotic behaviour of the Pearson random walks when the dimension d goes to infinity. Further, we investigate the same convergence result in a more general framework, where both the number and the lengths of the steps depend on the dimension. The results in the present paper can be applied to approximate the distribution of some classical Pearson random walk, for example, in the Dirichlet case.
ER  -