Matrix Whittaker processes

Abstract We study a discrete-time Markov process on triangular arrays of matrices size $$d\ge 1$$ d ≥ 1 , driven by inverse Wishart random matrices. The components the right edge evolve as multiplicative walks positive definite with one-sided interactions and can be viewed d -dimensional generalisation log-gamma polymer partition functions. establish intertwining relations to prove that, for suitable initial configurations process, bottom has an autonomous Markovian evolution explicit transition kernel. then show special singular configuration, fixed-time law is matrix Whittaker measure, which we define. To achieve this, perform Laplace approximation that requires solving constrained minimisation problem certain energy functions arguments directed graphs.