Convergence and limits of finite trees

2020/01/03 by Elek, Gábor, Tardos, Gábor
#05C05 (primary) 05C12 (secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.00905

Abstract

Motivated by the work of Lovász and Szegedy on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. Based on separable real trees, we introduce the notion of a dendron and show that the limits of finite trees are exactly the dendrons. We also prove that the limit dendron is unique.

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