The authors give effective Lévy-Khintchine theorems in higher-dimensional Diophantine approximation and central limit theorems for best approximations via homogeneous dynamics techniques.
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Proves limiting measures for joint equidistribution of ε-Diophantine approximates of matrices for almost every matrix, including first treatment of the multiplicative case via Poincaré sections and multiple mixing.
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L\'{e}vy-Khintchine Theorems: effective results and central limit theorems
The authors give effective Lévy-Khintchine theorems in higher-dimensional Diophantine approximation and central limit theorems for best approximations via homogeneous dynamics techniques.
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Counting and Joint equidistribution of approximates
Proves limiting measures for joint equidistribution of ε-Diophantine approximates of matrices for almost every matrix, including first treatment of the multiplicative case via Poincaré sections and multiple mixing.