From Plato’s search for hidden forms to Bernoulli’s law of large numbers and Markov’s breakthrough on dependent events, this story traces how mathematicians discovered the patterns hidden inside ...

Quantum Markov chains (QMCs) represent a natural quantum extension of classical Markov processes, encapsulating memoryless dynamics within quantum systems. They offer a powerful framework to model non ...

High-order Markov chain models extend the conventional framework by incorporating dependencies that span several previous states rather than solely the immediate past. This extension allows for a ...