{"ID":2841951,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.17575","arxiv_id":"2511.17575","title":"Random Text, Zipf's Law, Critical Length,and Implications for Large Language Models","abstract":"We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this symbol-level framework, which assumes no morphology, syntax, or semantics, we derive several structural results. First, word lengths follow a geometric distribution governed solely by the probability of the space symbol. Second, the expected number of words of a given length, and the expected number of distinct words of that length, admit closed-form expressions based on a coupon-collector argument. This yields a critical word length k* at which word types transition from appearing many times on average to appearing at most once. Third, combining the exponential growth of the number of possible strings of length k with the exponential decay of the probability of each string, we obtain a Zipf-type rank-frequency law p(r) proportional to r^{-alpha}, with an exponent determined explicitly by the alphabet size and the space probability. Our contribution is twofold. Mathematically, we give a unified derivation linking word lengths, vocabulary growth, critical length, and rank-frequency structure in a single explicit model. Conceptually, we argue that this provides a structurally grounded null model for both natural-language word statistics and token statistics in large language models. The results show that Zipf-like patterns can arise purely from combinatorics and segmentation, without optimization principles or linguistic organization, and help clarify which phenomena require deeper explanation beyond random-text structure.","short_abstract":"We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this symbol-level framework, which assumes no morphology, syntax, or semantics, we derive se...","url_abs":"https://arxiv.org/abs/2511.17575","url_pdf":"https://arxiv.org/pdf/2511.17575v1","authors":"[\"Vladimir Berman\"]","published":"2025-11-14T23:05:59Z","proceeding":"cs.CL","tasks":"[\"cs.CL\",\"stat.ME\",\"stat.ML\",\"stat.OT\"]","methods":"[\"Language Model\",\"Generative Adversarial Network\"]","has_code":false}