Discover how Markov chains predict real systems, from Ulam and von Neumann’s Monte Carlo to PageRank, so you can grasp ...

For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive ...

We build optimal exponential bounds for the probabilities of large deviations of sums $\sum_{k=1}^n f(X_k)$ where (Xk) is a finite reversible Markov chain and f is an arbitrary bounded function. These ...