The rain over Cambridge was the kind that didn’t fall so much as seep—into coats, into bones, into the very margins of notebooks left too long on park benches. Professor Alistair Norris, aged forty-seven, holder of the Chair in Stochastic Processes, stood at the window of his college rooms and watched the students scatter like particles undergoing Brownian motion.
The Unexpected Intersection: Understanding "Markov Chain Norris" markov chain norris
Norris defines a discrete-time Markov Chain $(X_n) {n \geq 0}$ as a random process satisfying the : $$P(X {n+1} = j \mid X_n = i, X_{n-1} = i_{n-1}, \dots, X_0 = i_0) = P(X_{n+1} = j \mid X_n = i)$$ In plain English: The future depends on the past only through the present. Once you know where you are right now, the history of how you got there is irrelevant to where you go next. The rain over Cambridge was the kind that
“I should have come sooner,” he said. “I should have never stopped.” Once you know where you are right now,