映射类群上有限支集分布的调和测度是奇异的
Harmonic measures for distributions with finite support on the mapping class group are singular
摘要：
Kaimanovich和Masur证明了对于一个具有有限一阶矩的初始分布，其支持生成一个非初等子群的映射类群上的随机游动，几乎必然收敛于表面上的投影测量叶理空间PMF中的一个点。这定义了PMF上的调和测度。在这里，我们证明了当初始分布具有有限支撑时，相应的调和测度关于PMF上的自然勒贝格测度是奇异的。
英文摘要：
Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on PMF. Here, we show that when the initial distribution has finite support, the corresponding harmonic measure is singular with respect to the natural Lebesgue measure on PMF.
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