Dr. Fengcheng Lin Profile

Dr. Fengcheng Lin

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Proceedings Article | 22 April 2022 Paper

A model can describe large networks

Fengcheng Lin

Proceedings Volume 12163, 1216319 (2022) https://doi.org/10.1117/12.2627298

KEYWORDS: Probability theory, Mathematical modeling

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In this article, we focus on Bernoulli percolation and mainly investigate bounds of the probability of the connectivity of 0 to the distance n. At first, we give a rough bound of the probability, and then refine our result by the high-dimensional RSW theory, which gives a nontrivial bound for a short crossing in ℤ^𝒅, as well as the renormalization method. We finish the last step of this section by coupling. Next, we give a more refined bound in ℤ^𝟐 using the dual graph. At last, we investigate the behaviors of some subgraphs of ℤ^𝟐. The work done and conclusions made in this article are fundamental in percolation theory. The purpose of this article is to introduce Bernoulli percolation in a relatively thorough way to the beginners of percolation theory and provide some insights into different proofs of basic conclusions.

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