Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Matrix Dirichlet processes

Songzi Li

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Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the theory of boundary equations, we describe Dirichlet processes on the matrix simplex and provide two models of matrix Dirichlet processes, which can be realized by various projections, through the Brownian motion on the special unitary group and also through Wishart processes.


Les processus de Dirichlet matriciels, en référence à leur mesure réversible, apparaissent de manière naturelle dans de nombreux modèles différents en probabilité. En utilisant la langage des opérateurs de diffusion et la théorie des équations de bord, nous décrivont les processus de Dirichlet sur le simplexe matriciel et proposont deux modèles pour les processus de Dirichlet matriciels, qui peuvent être réalisés par les projections diverses, par le movement brownien sur le groupe unitaire spécial et par les processus de Wishart.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 55, Number 2 (2019), 909-940.

Received: 25 September 2017
Revised: 18 January 2018
Accepted: 27 March 2018
First available in Project Euclid: 14 May 2019

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Digital Object Identifier

Primary: 47B25: Symmetric and selfadjoint operators (unbounded) 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Matrix Dirichlet processes Diffusion operators Wishart processes


Li, Songzi. Matrix Dirichlet processes. Ann. Inst. H. Poincaré Probab. Statist. 55 (2019), no. 2, 909--940. doi:10.1214/18-AIHP903.

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