Markovian Analysis in Language Modeling:

AbstractThis paper formalizes a mathematical framework for analyzing textual structure through the application of Markovian constraints in language modeling (Bonlarron & Régin, 2024). By leveraging n-gram probability distributions, we examine the structural indicators of text generation across two key dimensions: local predictability, quantified via perplexity (Cai & Cui, 2023), and global lexical distribution, quantified via statistical burstiness (Cummins, 2017). We demonstrate how the Markov assumption isolates local context to calculate conditional token probabilities using Maximum Likelihood Estimation (MLE) (Bonlarron & Régin, 2024). Furthermore, we model the inter-arrival times of lexical tokens to contrast the highly uniform, low-burstiness distributions characteristic of contemporary large language models (LLMs) with the high-variance, bursty patterns indicative of human authorship (Cai & Cui, 2023). The theoretical framework, mathematical models, and analytical matrices within this work were established through an interactive computational workflow directed by the author. Generative digital tools were utilized to execute structural modeling, mathematical formalization, and manuscript synthesis under the continuous direction, parameter constraints, and analytical validation of the author. This comprehensive framework provides a foundational methodology for computational stylistics, information theory, and cryptographic text authentication.