# Optimal bounds for bit-sizes of stationary distributions in finite Markov chains

@article{Skomra2021OptimalBF, title={Optimal bounds for bit-sizes of stationary distributions in finite Markov chains}, author={Mateusz Skomra}, journal={ArXiv}, year={2021}, volume={abs/2109.04976} }

An irreducible stochastic matrix with rational entries has a stationary distribution given by a vector of rational numbers. We give an upper bound on the lowest common denominator of the entries of this vector. Bounds of this kind are used to study the complexity of algorithms for solving stochastic mean payoff games. They are usually derived using the Hadamard inequality, but this leads to suboptimal results. We replace the Hadamard inequality with the Markov chain tree formula in order to…

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