Effective Density of Non-Degenerate Random Walks on Homogeneous Spaces

We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random...

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Veröffentlicht in:	International mathematics research notices 2024-06, Vol.2024 (11), p.9218-9236
Hauptverfasser:	Kim, Wooyeon, Kogler, Constantin
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description	We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting the spectral gap of the associated convolution operator.
doi_str_mv	10.1093/imrn/rnae011
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title	Effective Density of Non-Degenerate Random Walks on Homogeneous Spaces
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