Explore a framework for studying discrete Markov chains with particle interactions in this 37-minute USC Probability and Statistics Seminar talk. Delve into a novel holomorphic observable for transition probabilities, focusing on interactions of random matrix type. Examine the application of this approach to inhomogeneous (q,kappa)-distributions on lozenge tilings, uncovering their complex asymptotic behavior. Gain insights into the dynamic loop equation and its relevance to Berkeley's research in this field.