Convergence and limits of finite trees

Elek, Gabor and Tardos, Gabor (2022) Convergence and limits of finite trees. Combinatorica, 42 (6). pp. 821-852. ISSN 0209-9683

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Abstract

Motivated by the work of Lovász and Szegedy on the convergence and limits of dense graph sequences [10], we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. We introduce dendrons (a notion based on separable real trees) and show that the sampling limits of finite trees are exactly the dendrons. We also prove that the limit dendron is unique.