Abstract
Extending a construction of Bourgain for SL(2,R), we construct on any semisimple real Lie group G a symmetric probability measure whose stationary measure on the Furstenberg boundary has a smooth density and whose support is finite and generates a dense subgroup of G.
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Benoist, Y., Quint, JF. On the regularity of stationary measures. Isr. J. Math. 226, 1–14 (2018). https://doi.org/10.1007/s11856-018-1689-x
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DOI: https://doi.org/10.1007/s11856-018-1689-x