Markov Chains and GCD: Randomness Solves Number Theory
Markov chains are stochastic processes defined by memoryless transitions between states, where the next state depends only on the current one. This property makes them powerful tools for modeling systems with apparent randomness yet underlying structure—particularly relevant in number theory, where integer sequences often exhibit unpredictable yet statistically regular patterns. The steady-state distribution captures long-term behavior, enabling predictions from chaotic initial conditions. By embedding probabilistic models within deterministic number sequences, researchers unlock new insights into primality, randomness, and computational efficiency. What Are Markov Chains and Why Do They Matter in…
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