The Heckman-Opdam Markov processes

DOI10.1007/s00440-006-0034-1zbMath1123.58022arXivmath/0605020OpenAlexW2154856320MaRDI QIDQ880941

Bruno Schapira

Publication date: 21 May 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605020

zbMATH Keywords

Markov processesDirichlet formsroot systemslimit theoremsDunkl processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Brownian motion (60J65) Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65) Functional limit theorems; invariance principles (60F17)

Related Items (15)

Elementary symmetric polynomials and martingales for Heckman-Opdam processes ⋮ The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime ⋮ Random walk on a building of type \(\tilde A_r\) and Brownian motion of the Weyl chamber ⋮ Some martingales associated with multivariate Jacobi processes and Aomoto's Selberg integral ⋮ General β-Jacobi Corners Process and the Gaussian Free Field ⋮ Strong solutions to a beta-Wishart particle system ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ Affine Dunkl processes of type \(\widetilde{\mathrm{A}}_{1}\) ⋮ Multidimensional Yamada-Watanabe theorem and its applications to particle systems ⋮ An Introduction to Dunkl Theory and Its Analytic Aspects ⋮ β-Jacobi processes ⋮ Some martingales associated with multivariate Bessel processes ⋮ Functional central limit theorems for multivariate Bessel processes in the freezing regime ⋮ Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions ⋮ Radial Dunkl processes: existence, uniqueness and hitting time

Cites Work

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• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• Brownian bridge on Riemannian symmetric spaces
• Conformal restriction: The chordal case
• Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
• Paley–Wiener theorems for the Dunkl transform

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