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Independence Threshold for Collision Times of Many Planar Random Walks — arXiv:2609.21937

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21937
License (as archived): CC0-1.0
Archived: 2026-10-10T02:07:21.738Z
SHA-256 of the archived text: 77720006f3570db75d9307394bca3bd9a9e53b86fe888010cd363681ec7c64d2
Stable URL of this page: https://metraipolis.com/documento/dc_008decd69937

How to cite

Independence Threshold for Collision Times of Many Planar Random Walks — arXiv:2609.21937 — arXiv (en), https://arxiv.org/abs/2609.21937 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_008decd69937 (Metraipolis archive dc_008decd69937, sha256 77720006f3570db75d9307394bca3bd9a9e53b86fe888010cd363681ec7c64d2)

BibTeX

@misc{dc008decd69937,
  title = {Independence Threshold for Collision Times of Many Planar Random Walks — arXiv:2609.21937},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21937},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_008decd69937; sha256 77720006f3570db75d9307394bca3bd9a9e53b86fe888010cd363681ec7c64d2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21937. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study collision times of many independent simple random walks on $\mathbb Z^2$ through the joint moment generating function of their pairwise collision local times. For a fixed number of walks, these collision times are known to be asymptotically independent after a suitable logarithmic normalisation. We investigate the extent to which this independence persists when the number of walks grows. For $N$ being the walk length, our results identify a threshold $\asymp (\log N)^{\frac{1}{3}}$, on which the transition from independence to dependence happens. The proofs combine chaos expansion techniques and a correlation inequality, which is the result of a local limit theorem.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.PR).
Categorie arXiv: Probability (math.PR) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.21937 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T01:47:50.207Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).