Abstract
The usual analysis of random walk on graphs uses the usual eigenvectors (and eigenvalues). For absorbing Markov chains a different theory is available. In joint work with Laurent Miclo we have begun studying rates of convergence to quasi-stationarity. We have lots of examples and the start of a general theory, associating an ergodic chain to an absorbing chain in such a way that rates are comparable. There is lots to be done.