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Creators/Authors contains: "Hough, Robert"

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  1. ; (, Annales scientifiques de lÉcole normale supérieure)
    null (Ed.)
    We introduce a new method for proving central limit theorems for random walk on nilpotent groups. The method is illustrated in a local central limit theorem on the Heisenberg group, weakening the necessary conditions on the driving measure. As a second illustration, the method is used to study walks on the nn uni-upper triangular group with entries taken modulo p. The method allows sharp answers to the behavior of individual coordinates: coordinates immediately above the diagonal require order p^2 steps for randomness, coordinates on the second diagonal require order p steps; coordinates on the kth diagonal require order p^{2/k} steps. 
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  2. ; (, The Annals of Probability)
    null (Ed.)
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  3. ; (, Mathematics of Computation)
    null (Ed.)
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  4. (, Journal of Number Theory)
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  5. (, Research in the Mathematical Sciences)
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  6. ; (, Duke Mathematical Journal)
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  7. ; ; (, Communications in Mathematical Physics)
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  8. (, Probability Theory and Related Fields)
    A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorem of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis–Hough which treated general measures on the Heisenberg group. 
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  9. (, Electronic Journal of Probability)
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