2006/06/09 by Nizar Demni, Demni, Nizar · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.PR
paper · pdf · doi:10.48550/arxiv.math/0606218
23 pages
openalex publication_date 2006/06/09 · arxiv created 2007/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a matrix approach, we define the free Jacobi process as the limit of the complex Jacobi matrix process. The we derive a free SDE which is analogous to its classical counterpart. To proceed, we prove that fro suitable parameters the process remains injective if it is initially injective and then use the polar decomposition. In the stationnary case, this will be easily deduced from the explicit expression of the spectral measure. In the general setting we derive a recurrence formula for the moments. Moreover, a p. d. e. for the Cauchy transform of the law is given.