Monotone mobility matrices
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Abstract
The transition matrix of a discrete Markov chain is called monotone if each row stochastically dominates the row above it. Monotonicity is an ideal assumption to impose on a Markov chain model of mobility. Monotonicity is behaviorally weak yet mathematically strong. It is behaviorally weak in the sense that it is theoretically plausible and is empirically supported. It is mathematically strong in the sense that monotone Markov chains have a number of convenient mathematical properties. This paper reviews the convenient properties and applies the monotonicity concept to immobility measurement.