The top eigenvalue of uniformly random trees

Louigi Addario-Berry, Gábor Lugosi, Roberto Imbuzeiro Oliveira

Let ${\mathbf{T}}_n$ be a uniformly random tree with vertex set $[n]=\{1,\dots ,n\}$, let ${\Delta }_{{\mathbf{T}}_n}$ be the largest vertex degree in ${\mathbf{T}}_n$, and let $λ_1({\mathbf…