there are many well-known concentration results for sums of independent random matrices, e.g. those of rudelson, ahlswede-winter, tropp, and oliveira. we move beyond the independent setting, and prove a chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an reversible markov chain, confirming a conjecture due to wigderson and xiao. our proof is based on a new multi-matrix extension of the golden-thompson inequality which follows from complex interpolation methods. joint work with a. garg, y. lee, and z. song.