Schröder's problems and scaling limits of random trees

Jim Pitman; Douglas Rizzolo

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arXiv · 1107.1760

Schröder's problems and scaling limits of random trees

Jim Pitman·Douglas Rizzolo

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Abstract

In a classic paper Schröder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on average. For each of the four problems we prove that a uniform pick from the appropriate set of bracketings, when considered as a tree, has the Brownian continuum random tree as its scaling limit as the size of the word or set goes to infinity.

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Jim Pitman, Douglas Rizzolo. 2013-09-22. Schröder's problems and scaling limits of random trees. https://arxiv.org/abs/1107.1760

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