1. Introduction: Markov Chains as Engines of Randomness in Interactive Systems Markov chains serve as foundational models for structured randomness in interactive systems, where each state transition depends only on the current state—embodying the principle of memorylessness. A Markov chain is defined by a finite or countable set of states and probabilistic rules governing movement between them, formalized as: P(Xₙ₊₁ = j | Xₙ = i) = P(j|i), independent of prior states. This property captures unpredictability while preserving continuity—essential for […]
