Local Convergence of Critical Random Trees and Continuous-State Branching Processes

Xin He ()
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Xin He: University of Science and Technology of China

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 685-713

Abstract: Abstract We study the local convergence of critical Galton–Watson trees and Lévy trees under various conditionings. Assuming a very general monotonicity property on the measurable functions of critical random trees, we show that random trees conditioned to have large function values always converge locally to immortal trees. We also derive a very general ratio limit property for measurable functions of critical random trees satisfying the monotonicity property. Finally we study the local convergence of critical continuous-state branching processes, and prove a similar result.

Keywords: Galton–Watson tree; Lévy tree; Conditioning; Local limit; Immortal tree; Height; Width; Total mass; Maximal degree; 60J80; 60F17 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01074-9

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