ENTANGLEMENT PERCOLATION AND SPHERES IN Z^d

ENTANGLEMENT PERCOLATION AND SPHERES IN Z^d

We obtain a new lower bound of 0.06576 for the 1-entanglement critical probability (in dimension 3), and prove that the critical point for the existence of a sphere surrounding the origin and intersecting only closed bonds in Z^d is greater than 1/8(d−1) , d ≥ 3. This substantially improves the prev...

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Veröffentlicht in:Electronic journal of probability 2022-07, Vol.27
1. Verfasser: Couronné, Olivier
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Probability
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Zusammenfassung:We obtain a new lower bound of 0.06576 for the 1-entanglement critical probability (in dimension 3), and prove that the critical point for the existence of a sphere surrounding the origin and intersecting only closed bonds in Z^d is greater than 1/8(d−1) , d ≥ 3. This substantially improves the previous lower bounds and gives the correct order of magnitude for large d.
ISSN:1083-6489
1083-6489
DOI:10.1214/22-EJP816