On coprime percolation, the visibility graphon, and the local limit of the GCD profile

DOI10.1214/21-ECP381zbMath1495.60093arXiv1804.06486OpenAlexW2797042057MaRDI QIDQ2078123

Sébastien Martineau

Publication date: 25 February 2022

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06486

zbMATH Keywords

graphonpercolationarithmeticlocal limitsvisible/primitive/coprime points

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Convergence of probability measures (60B10) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Limits, profinite groups (20E18)

Uses Software

• MathOverflow

Cites Work

• Ergodic properties of visible lattice points
• The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
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• Pointwise theorems for amenable groups.
• Visible lattice points in random walks
• Recurrence of distributional limits of finite planar graphs
• Deterministic percolation
• Entropy and diffraction of the \(k\)-free points in \(n\)-dimensional lattices
• ON THE MERTENS–CESÀRO THEOREM FOR NUMBER FIELDS
• Probability on Trees and Networks
• Visibility and Directions in Quasicrystals
• Graph limits and exchangeable random graphs
• Vertex-transitive graphs and vertex-transitive maps
• Lattice Point Visibility on Generalized Lines of Sight
• PROBABILISTIC PROOF OF LIMIT THEOREMS IN NUMBER THEORY BY MEANS OF ADELES
• Patterns of Visible and Nonvisible Lattice Points
• NOTE ON AN ASYMPTOTIC FORMULA CONNECTED WITH r-FREE INTEGERS
• Arithmetical Pattern Problems Relating to Divisibility by r th Powers^*
• A conjecture concerning a limit of non-Cayley graphs
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