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This research investigates the behavior of maximum cluster diameter in non-critical bond percolation.

December 22, 2025Open Access

Maximum Cluster Diameter in Non-Critical Bond Percolation

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This research reveals how maximum cluster diameter behaves in non-critical bond percolation, suggesting important asymptotic patterns.

This research investigates the behavior of maximum cluster diameter in non-critical bond percolation.
Studied independent Bernoulli bond percolation in dimensions d ≥ 2
Proved the relation R_n / log n → varkappa(p) almost surely
Established a large deviation principle for R_n > ρ log n when ρ > varkappa(p)
Analyzed asymptotics of clusters with large diameters
Identified a relationship between maximum diameter and logarithmic scales
Demonstrated exponential decay rates influence the maximum diameter
Provided insights into the frequency of large clusters in non-critical scenarios.

Ken‐ichiro Kobayashi (2025) studied this question.

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