We consider a singularly perturbed (finite state) Markov chain and provide a complete characterization of the fundamental matrix. In particular, we obtain a formula for the regular part simpler than a ...

A Markov chain is a mathematical concept of a sequence of events, in which each future event depends only on the state of the previous events. Like most mathematical concepts, it has wide-ranging ...

What if you could predict the future, not with a crystal ball, but with math? In this guide, Veritasium explains how a 120-year-old concept called Markov chains has become a silent force shaping ...

In this episode probability mathematics and chess collide. In this episode probability mathematics and chess collide. What is the average number of steps it would take before a randomly moving knight ...