High-Precision Entropy Values for Spanning Trees in Lattices
Jessica L. Felker, Russell Lyons
TL;DR
This paper introduces a new numerical technique for precisely calculating the exponential growth rate of spanning trees in Euclidean lattices, providing rigorous bounds and resolving previous open questions.
Contribution
A novel numerical method for more accurate evaluation of spanning tree growth rates in lattices, with rigorous error bounds and improved precision over prior results.
Findings
More precise exponential growth rate values
Rigorous bounds on numerical accuracy
Resolution of an open question by Shrock and Wu
Abstract
Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.
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