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This is a Quantitative Study study.

October 12, 2025Open Access

Limiting distribution of the chemical distance in high dimensional critical percolation

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Study reveals the limiting distribution of chemical distance in Bernoulli percolation, indicating its link to Brownian motion dynamics.

The study identifies the chemical distance limiting distribution in high-dimensional critical percolation.
As the distance between the origin and a distant vertex is rescaled, it converges to a specific distribution linked to Brownian motion.
This analysis utilizes a moment computation approach, leveraging the pivotal edges' additive structure.
The findings reinforce the significance of the incipient infinite cluster limit established in recent research.

Chatterjee et al. (2025) studied this question.

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