Omer Friedland, Ohad Giladi, Olivier Guédon
Published 2014-10-03Version 1
This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained by Friedland and Sodin and by Rudelson and Vershynin.
Yet another notion of irregularity through small ball estimates
Convex bodies generated by sublinear expectations of random vectors
Efficient simulation of density and probability of large deviations of sum of random vectors using saddle point representations
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