Leonhard Nagel

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math.PR2025

Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs

Leonhard Nagel

We study how eigenvectors of random regular graphs behave when projected onto fixed directions. For a random $d$ -regular graph with $N$ vertices, where the degree $d$ grows slowly…

math.PR2025

Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants

Leonhard Nagel

We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$ -regular graph on $N$ vertices with fixed $d \geq 3$ an…