Robust Mixing

In this paper, we develop a new "robust mixing" framework for reasoning about adversarially modified Markov Chains (AMMC). Let P be the transition matrix of an irreducible Markov Chain with stationary distribution . An adversary announces a sequence of stochastic matrices {At}t>0 satisfying At = . An AMMC process involves an application of P followed by At at time t. The robust mixing time of an ergodic Markov Chain P is the supremum over all adversarial strategies of the mixing time of the corresponding AMMC process. Applications include estimating the mixing times for certain non-Markovian processes and for reversible liftings of Markov Chains. Non-Markovian card shuffling processes: The random-to-cyclic transposition process is a non-Markovian card shuffling process, which at time t, exchanges the card at position Lt := t (mod n) with a random card. Mossel, Peres and Sinclair (2004) showed a lower bound of (0.0345 + o(1))n log n for the mixing time of the random-to-cyc...

• Type: Conference
• Year: 2006
• Where: APPROX
• Authors: Murali K. Ganapathy
• Keywords: Algorithms, APPROX 2006, Markov Chain, Mixing Time, Robust Mixing