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The Horton-Strahler analysis is a graph-theoretic method to measure thebifurcation complexity of branching patterns, by defining a number called theorder to each branch. The main result of this paper is a large deviationtheorem for the number of branches of each order in a random binary tree. Therate function associated with a large deviation cannot be derived in a closedform; instead, asymptotic forms of the rate function are given.

Large deviation theorem for branches of the random binary tree in the Horton-Strahler analysis