Scale-free Characteristics of Multilingual Legal Texts and the Limitations of LLMs

We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps' exponent β (vocabulary growth), Taylor's exponent α (word-frequency fluctuation scaling), compression rate r (redundancy), and entropy. Our corpora span three domains: legal documents (statutes, cases, deeds) as a specialized domain, general natural language texts (literature, Wikipedia), and AI-generated (GPT) text. We find that legal texts exhibit slower vocabulary growth (lower β) and higher term consistency (higher α) than general texts. Within legal domain, statutory codes have the lowest β and highest α, reflecting strict drafting conventions, while cases and deeds show higher β and lower α. In contrast, GPT-generated text shows the statistics more aligning with general language patterns. These results demonstrate that legal texts exhibit domain-specific structures and complexities, which current generative models do not fully replicate.