Diameter of Random Weighted Spanning Trees
Analysis
This paper investigates the diameter of random weighted uniform spanning trees. The key contribution is determining the typical order of the diameter under specific weight assignments. The approach combines techniques from Erdős-Rényi graphs and concentration bounds, offering insights into the structure of these random trees.
Key Takeaways
- •The paper analyzes the diameter of random weighted uniform spanning trees.
- •It establishes the typical order of the diameter under specific weight conditions.
- •The approach uses techniques from Erdős-Rényi graphs and concentration bounds.
- •The diameter is shown to be of order $n^{1/3} \log n$ with a $\log \log n$ correction.
Reference
“The diameter of the resulting tree is typically of order $n^{1/3} \log n$, up to a $\log \log n$ correction.”