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 ...

We focus our attention herein on a Markov chain $x_0, x_1, \cdots$ with a countable number of states indexed by a subset I of the integers and with stationary ...

We develop a new technique, based on Stein’s method, for comparing two stationary distributions of irreducible Markov chains whose update rules are close in a certain sense.We apply this technique to ...

Amid all the hype about AI it sometimes seems as though the world has lost sight of the fact that software such as ChatGPT contains no intelligence. Instead it’s an extremely sophisticated system for ...

Mathematics often seems like an abstract concept, but its applications can have profound impacts on the world around us. From predicting the next word in a sentence to understanding how Google’s ...