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#ConradMitzenmacher-6
"In this paper, we begin by reviewing the fascinating history of this fundamental problem. Then, we use methods from #ComplexAnalysis to prove that Miller’s random monkey experiment yields power laws for [the] rank-frequency distribution
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"In this paper, we begin by reviewing the fascinating history of this fundamental problem. Then, we use methods from #ComplexAnalysis to prove that Miller’s random monkey experiment yields power laws for [the] rank-frequency distribution
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>with probability assignments to keys satisfying a rationality assumption on log-ratios of pairs of probabilities.
We use analytic methods to establish a simple explicit power law in cases with rational log-ratios for pairs of probabilities; more specifically,
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We use analytic methods to establish a simple explicit power law in cases with rational log-ratios for pairs of probabilities; more specifically,
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>we use generalized Dirichlet series and an elementary identity established by means of Fourier series. Passing to a limit on these formulas predicts an analogous result in the remaining “irrational” cases, and this prediction agrees with an unpublished theorem..by Montgomery;
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