Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees (Q2570830)

This paper studies the asymptotics of the \textbf{p}-mapping model of a random mapping on \([n]\) as \(n\) gets large, under a large class of asymptotic regimes for the underlying distribution \textbf{p}. The authors encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived from a bridge with exchangeable increments. Their setting generalizes previous results by allowing a finite number of ``attracting points'' to emerge.