Abstract
The sprout, a tree growing in real time is introduced. The sprout is a generalization and an embedding in time of the standard recursive tree. The sprout is proposed as a model for the growth of the Internet. The tree size is analyzed via an associated two-color stochastic process (the sprout process), which is a special case of the Polya process. Owing to its potential as a modeling tool, the more general Polya process is analyzed on average. In addition to the usage of the Polya process in evaluating sprouts, we also give a heuristic interpretation of the result for Polya urns, which might be a first step toward understanding several nonclassic urn models, as those with nonconstant row sum and those with multiple eigenvalues.
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