Work

Moderate deviations and laws of the iterated logarithm for geometric functionals in the sparse regime

Year: 2026

Type: preprint

Abstract: We prove moderate deviation principles and laws of the iterated logarithm in the sparse regime for geometric and topological functionals associated with $k$-point connected components. These limit theorems are established at both the measure-valued and vector-valued levels, for Poisson and binomial point processes. As applications, we derive corresponding results for component counts in random geometric graphs and Čech complexes and for counts of Morse critical points.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.14923

Authors: Sakihara, Yudai, Tsunoda, Kenkichi

Institution: Kyushu University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science

Award: Scaling limit for lattice-gas via precise estimates on relative entropies

OpenAlex ID: W7213267593

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