Strong stationary duality for Möbius monotone Markov chains: Examples
Słowa kluczowe:
Markov chains, stochastic monotonicity, eigenvalues, Möbius monotonicity, strong stationary duality, strong stationary times, separation distance, mixing time, Ising model, hypercubeAbstrakt
We construct strong stationary dual chains for nonsymmetric random walks on square lattice, for random walks on hypercube and for some Ising models on the circle. The strong stationary dual chains are all sharp and have the same state space as original chains. We use Möbius monotonicity of these chains with respect to some natural orderings of the corresponding state spaces. This method provides an alternative way to study mixing times for studied models.
