Local convergence of critical Galton-Watson trees (Q6617599)

The paper studies local convergence of critical Galton-Watson trees. Let \(T\) be the set of trees and \(A\) be an integer-valued function defined on \(T\) which is finite on \(T_0\), which is the subset containing finite trees. It presents a general result concerning the local convergence of critical and subcritical Galton-Watson trees conditioned on \(A_n=\{t\in T: A(t)\in[n,n+n_0)\}\) toward Kesten's tree, where \(n_0\) is an given non-negative integer or positive infinity, and \(n\) is a positive integer. The result is applied to the conditioning on large width in the critical case.