# The cutoff phenomenon for ergodic Markov processes

@article{Chen2008TheCP,
title={The cutoff phenomenon for ergodic Markov processes},
author={G. Chen and L. Saloff-Coste},
journal={Electronic Journal of Probability},
year={2008},
volume={13},
pages={26-78}
}
• Published 2008
• Mathematics
• Electronic Journal of Probability
• We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian motion on families of compact Riemannian manifolds. We give criteria for the existence of a cutoff when convergence is measured in $L^p$-norm, $1 < p < \infty$. This allows us to prove the existence of a cutoff in cases where the cutoff time is not explicitly known. In the reversible case, for \$1 < p… CONTINUE READING