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This is a Quantitative Study study.

September 26, 2025Open Access

Asymptotic expansion of the critical point for oriented percolation in high dimensions

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The asymptotic expansion of the critical point shows behavior aligning with powers of d^{-1}, enhancing mathematical understanding.
Analysis reveals how the critical point evolves as dimensions increase, characterizing its dependency on d.
This method utilizes the lace expansion, providing a novel approach to study percolation in high dimensions.
Findings offer implications for theoretical models of percolation, potentially guiding future mathematical explorations.

Implication

Analysis of critical points in oriented percolation reveals asymptotic behavior, suggesting new insights.

Abstract

We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on Zᵈ in powers of d⁻¹ as d→ ∞. The proof relies heavily on the lace expansion.

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Cite This Study

Noboru Kawamoto (2025) studied this question.

synapsesocial.com/papers/68d6cd5bb1249cec298b3451 https://doi.org/10.48550/arxiv.2508.12299

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Implication

Analysis of critical points in oriented percolation reveals asymptotic behavior, suggesting new insights.

Abstract

We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on Zᵈ in powers of d⁻¹ as d→ ∞. The proof relies heavily on the lace expansion.

Asymptotic expansion of the critical point for oriented percolation in high dimensions

Key Points

Implication

Abstract

Discussion

Cite This Study

Asymptotic expansion of the critical point for oriented percolation in high dimensions

Key Points

Implication

Abstract

Discussion

Cite This Study

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