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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
62/2020

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

Marc Peigne and Tat Dat Tran

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.

Received:
Jun 3, 2020
Published:
Jun 3, 2020
MSC Codes:
60J05, 60F05
Keywords:
Iterated function systems, quasi-compact linear operators, absorbing compact set, invariant probability measure, invariant probability density

Related publications

inJournal
2022 Repository Open Access
Marc Peigne and Tat Dat Tran

On the asymptotic behavior of the Diaconis-Freedman chain in a multi-dimensional simplex

In: Journal of applied probability, 59 (2022) 2, pp. 505-526