An effective multi-equidistribution result for diagonal translates of unipotent flows is established, yielding a central limit theorem in inhomogeneous Diophantine approximation for non-Liouville shifts.
Non-Expanding Random walks on Homogeneous spaces and
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Upper bounds are established for the dimension of singular-on-average and ω-singular affine forms in singly metric Diophantine approximation, with extensions to weighted cases and fractal intersections.
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Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation
An effective multi-equidistribution result for diagonal translates of unipotent flows is established, yielding a central limit theorem in inhomogeneous Diophantine approximation for non-Liouville shifts.
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Dimension bounds for singular affine forms
Upper bounds are established for the dimension of singular-on-average and ω-singular affine forms in singly metric Diophantine approximation, with extensions to weighted cases and fractal intersections.