Abstract
This note is inspired by [BZ], which describes the true shape of a tree. Each planar tree (remember that a planar tree is a tree in which, for each vertex, the adjacent edges are cyclically ordered) has a distinguished embedding in the complex plane (up to similitude).
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Bétréma, J., Zvonkin, A.: La vraie forme d'un arbre. TAPSOFT '93: theory and practice of software development (Orsay, 1993), 599–612, Lecture Notes in Comput. Sci., 668, Springer, Berlin, 1993. 05C05.
Doob, J.L.: Classical potential theory and its probabilistic counterpart. Grundlehren der Mathematischen Wissenschaften, 262. Springer-Verlag, New York, 1984.
Lando, S., Zvonkin, A.: Graphs on surfaces and their applications, Encyclopedia of Mathematical Sciences, Low dimensional topology, II. Springer-Verlag, berlin, Heidelberg, 2004.
Marshall, D.E.; Rohde, S.: The Löwner differential equation and slit mappings. J. Amer. Math. Soc. 18 (2005), no. 4, 763–778.
Rudin, W.: Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.
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Biane, P. (2009). Shabat polynomials and harmonic measure. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_5
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