On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex

Marc Peigné; Tat Dat Tran

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arXiv · 2006.02069

On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex

Marc Peigné·Tat Dat Tran

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Abstract

In this paper, we give out a setting of an Diaconis and Freedman's chain in a multidimensional simplex and consider its asymptotic behavior. By using techniques in random iterated functions theory and quasi-compact operators theory, we first give out some sufficient conditions which ensure the existence and uniqueness of an invariant probability measure. In some particular cases, we give out explicit formulas of the invariant probability density. Moreover, we completely classify all behaviors of this chain in dimensional two. Eventually, some other settings of the chain are discussed.

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Marc Peigné, Tat Dat Tran. 2020-06-03. On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex. https://arxiv.org/abs/2006.02069

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