Abstract.
Consider a central Gaussian convolution semigroup (μ t ) t > 0 on a connected compact semisimple group. Then either the measure μ t is singular with respect to Haar measure for all t > 0, or there exists a time t such that μ t is absolutely continuous with respect to Haar measure and admits a continuous density.
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Received: 6 November 2001 / Revised version: 13 June 2002 / Published online: 30 September 2002
Research partially supported by NSF grant DMS 0102126
Mathematics Subject Classification (2000): 28C10, 28C20, 60B15, 60G30
Keywords or phrases: Gaussian convolution semigroups – Dichotomy – Absolute continuity
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Bendikov, A., Saloff-Coste, L. Some dichotomy results for central Gaussian convolution semigroups on compact groups. Probab Theory Relat Fields 124, 561–573 (2002). https://doi.org/10.1007/s00440-002-0228-0
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DOI: https://doi.org/10.1007/s00440-002-0228-0
Keywords
- Convolution
- Compact Group
- Dichotomy Result
- Continuous Density
- Semisimple Group