On the hypergroup property

Laurent Miclo (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

The hypergroup property satisfied by certain reversible Markov chains can be seen as a generalization of the convolution related features of class random walks on groups. Carlen, Geronimo and Loss~\cite{MR2764893} developed a method for checking this property in the context of Jacobi eigen-polynomials. A probabilistic extension of their approach is proposed here, enabling to recover the discrete example of the biased Ehrenfest model due to Eagleson \cite{MR0328162}. Next a spectral characterization is provided for finite birth and death chains enjoying the hypergroup property with respect to one of the boundary points.

Mots clés: Dirichlet (minor) eigenvalues; biaised Ehrenfest model; hypergroup property; finite reversible Markov processes; Neumann eigenvectors; finite birth and death processes

Domaines: Probabilités [math.PR]

Laurent Miclo. On the hypergroup property. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2017, 26 (2), pp.417-435. ⟨hal-01117051⟩