Zipf Distributions from Two-Stage Symbolic Processes: Stability Under Stochastic Lexical Filtering

Vladimir Berman
11/26/2025
stat.MEcs.CLstat.ML

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Abstract

Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite alphabet, generating a geometric distribution of word lengths. Interacting exponential forces yield a power-law rank-frequency curve, determined by alphabet size and blank symbol probability. Simulations support predictions, matching English, Russian, and mixed-genre data. The symbolic model suggests Zipf-type laws arise from geometric constraints, not communicative efficiency.

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Cite this paper

@article{berman2025zipf,
  title  = {Zipf Distributions from Two-Stage Symbolic Processes: Stability Under Stochastic Lexical Filtering},
  author = {Vladimir Berman},
  year   = {2025},
  eprint = {2511.21060},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2511.21060v1}
}

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