A homological upper bound on critical probabilities for hyperbolic percolation

Abstract

We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the infinite graphs.

References in corpus (3)

• Percolation on hyperbolic lattices
• Crossing on hyperbolic lattices
• Bounds of percolation thresholds on hyperbolic lattices

Cited by in corpus (3)

• Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
• Locality of percolation critical probabilities: uniformly nonamenable case
• Homology-changing percolation transitions on finite graphs