TL;DR
This paper explores the relationships between critical percolation probabilities, the uniqueness of infinite clusters, and graph limits, providing partial results to understand their interconnections.
Contribution
It introduces new insights into how critical probabilities relate to graph limits and percolation properties, with partial results advancing theoretical understanding.
Findings
Established links between critical probabilities and graph limits
Provided partial results on percolation and cluster uniqueness
Enhanced theoretical framework for percolation on infinite graphs
Abstract
A question relating the critical probability for percolation, the critical probability for a unique infinite cluster and graph limits is presented, together with some partial results.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Mathematical Dynamics and Fractals