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math.PR2015★ 2 cited
A note on the maximal out-degree of Galton-Watson trees
Xin He
In this note we consider both the local maximal out-degree and the global maximal out-degree of Galton-Watson trees. In particular, we show that the tail of any local maximal out-d…
math.PR2015★ 3 cited
Local convergence of critical random trees and continuous-state branching processes
Xin He
We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random…