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Contents of PMS, Vol. 36, Fasc. 1,
pages 75 - 97
 

STRONG STATIONARY DUALITY FOR MÖBIUS MONOTONE MARKOV CHAINS: EXAMPLES

Paweł Lorek
Ryszard Szekli

Abstract: We construct strong stationary dual chains for non-symmetric 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.

2000 AMS Mathematics Subject Classification: Primary: 60J10; Secondary: 06A06, 60G40.

Keywords and phrases: Markov chains, stochastic monotonicity, eigenvalues, Möbius monotonicity, strong stationary duality, strong stationary times, separation distance, mixing time, Ising model, hypercube.

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