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

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This is a Quantitative Study study.

Noboru Kawamoto

doi:10.48550/arxiv.2508.12299

August 17, 2025Open Access

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

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Key Points

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.

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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.

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

Key Points

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Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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