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A lower bound for the critical probability of the square lattice site percolation

✍ Scribed by Bálint Tóth

Publisher
Springer
Year
1985
Tongue
English
Weight
164 KB
Volume
69
Category
Article
ISSN
1432-2064

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📜 SIMILAR VOLUMES

A new lower bound for the critical proba
A new lower bound for the critical probability of site percolation on the square lattice
✍ J. van den Berg; A. Ermakov 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 705 KB

The critical probability for site percolation on the square lattice is not known exactly. Several authors have given rigorous upper and lower bounds. Some recent lower bounds are (each displayed here with the first three digits) 0.503 (Toth [13]), 0.522 (Zuev [15]), and the best lower bound so far,

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## Abstract A critical set is a partial latin square that has a unique completion to a latin square, and is minimal with respect to this property. Let __scs__(__n__) denote the smallest possible size of a critical set in a latin square of order __n__. We show that for all __n__, $scs(n)\geq n\lfloo