Expansion for the critical point of site percolation: the first three terms-Reference-Cited by-同舟云学术

Expansion for the critical point of site percolation: the first three terms

Published:2021-09-28 Issue: Volume: Page:1-25
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

Heydenreich Markus,Matzke Kilian

Abstract

Abstract We expand the critical point for site percolation on the d-dimensional hypercubic lattice in terms of inverse powers of 2d, and we obtain the first three terms rigorously. This is achieved using the lace expansion.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference17 articles.

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2. Critical Site Percolation in High Dimension

3. Asymptotic expansions inn−1 for percolation critical values on then-Cube and ℤn

4. Expansion in ${\boldsymbol{n^{-1}}}$ for Percolation Critical Values on the $n$-cube and ${\boldsymbol{{\mathbb Z}^n}}$: the First Three Terms

5. Critical percolation in high dimensions

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