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.
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The first author was partially supported by the ERC Consolidator Grant “Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces” No. 648017 and by the ERC Synergy Grant “Dynasnet” No. 810115.
The second author was partially supported by the ERC Synergy Grant “Dynasnet” No. 810115, the ERC advanced grant “GeoSpace” No. 882971, the National Research, Development and Innovation Office NKFIH projects K-116769, K-132696, KKP-133864, SNN-117879, SSN-135643 and by the grant of Russian Government N 075-15-2019-1926.
