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Award ID contains: 1855575

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  1. ; ; (, Combinatorics probability and computing)
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  2. ; (, Theory of probability and its applications)
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  3. ; ; (, Springer proceedings in mathematics)
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  4. ; ; (, Springer proceedings in mathematics)
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  5. ; (, The annals of applied probability)
    We present a short and elementary proof of the Ajtai-Koml\'os-Tusn\'ady (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound applies to more general families of samples, including dependent variables, of interest in the study of rates of convergence for empirical measures. Following the recent pde approach by L. Ambrosio, F. Stra and D. Trevisan, we also adapt a simple proof of the lower bound. 
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  6. ; (, International mathematics research notices)
    null (Ed.)
    We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise. 
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  7. ; ; (, Electronic journal of probability)
    null (Ed.)
    Under Poincare-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional Euclidean spheres, the results extend and refine previous results to non-symmetric models. 
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  8. ; (, Journal of fourier analysis applications)
    null (Ed.)
    We explore upper bounds on Kantorovich transport distances between probability measures on the Euclidean spaces in terms of their Fourier-Stieltjes transforms, with focus on non-Euclidean metrics. The results are illustrated on empirical measures in the optimal matching problem on the real line. 
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  9. (, Lecture notes in mathematics)
    B. Klartag, E. Milman (Ed.)
    We consider rates of approximation of distributions of weighted sums of independent, identically distributed random variables by the Edgeworth correction of the 4-th order. 
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  10. ; ; (, The Annals of probability)
    null (Ed.)
    Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures. 
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