arXiv Open Access 2025

Strassen's LIL and a Phase transition for the capacity of the random walk under diameter constraints

Arka Adhikari Izumi Okada

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Abstrak

We discuss the relationship between the capacity and the geometry for the range of the random walk for $d=3$. In particular, we consider how efficiently the random walk moves or what shape it forms in order to maximize its capacity. In one of our main results, we show a functional law for the capacity of the random walk. In addition, we find that there is a phase transition for the asymptotics of the capacity of the random walk when we condition the diameter of the random walk.

Topik & Kata Kunci

math.PR

Penulis (2)

Arka Adhikari

Izumi Okada

Format Sitasi

APA MLA BibTeX

Adhikari, A., Okada, I. (2025). Strassen's LIL and a Phase transition for the capacity of the random walk under diameter constraints. https://arxiv.org/abs/2503.12728

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓