Zipf's Law Leads to Heaps' Law¶
Lü, Zhang, & Zhou. (2010). Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems.
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Domain-specific¶
- Heaps' Law
- The mechanism behind the regularity is the Zipfian rank-frequency distribution of words: when the r-th most common word has frequency proportional to 1/r^α with α > 1, the expected type count at sample size N grows asymptotically as N^(1/α), so β = 1/α in the large-sample limit and the two laws are analytically coupled
This sourceLü, Zhang & Zhou (2010) establish that β=1/α is an asymptotic, large-size-limit relation that degenerates to β=1 for α≤1; the two-regime core-lexicon/rare-tail account of natural-language Zipf exponents used here to reconcile that coupling with observed β≈0.4–0.6 is not this paper's finding and needs a separate source (e.g., empirical work on the two-piece structure of word-frequency rank curves).
- The mechanism behind the regularity is the Zipfian rank-frequency distribution of words: when the r-th most common word has frequency proportional to 1/r^α with α > 1, the expected type count at sample size N grows asymptotically as N^(1/α), so β = 1/α in the large-sample limit and the two laws are analytically coupled
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