T. Juvskevivcius

activity

20112022

most citedSmall ball probabilities, maximum density and rearrangements

2 citations · 3 across the 4 of their papers we have counts for

collaborators

4 papers

math.PR2022

The sharp form of the Kolmogorov--Rogozin inequality and a conjecture of Leader--Radcliffe

Tomas Juškevičius

Let $X$ be a random variable and define its concentration function by $Q_{h} (X) = x \in R sup P (X \in (x, x + h]) .$ For a sum $S_{n} = X_{1} + \dots + X_{n}$ of indep…

math.PR2019★ 1 cited

On Littlewood-Offord theory for arbitrary distributions

Tomas Juškevičius, Valentas Kurauskas

Let $X_{1}, \dots, X_{n}$ be independent identically distributed random vectors in $R^{d}$ . We consider upper bounds on $max_{x} P (a_{1} X_{1} + \dots + a_{n} X_{n} = x)$ under various…

math.PR2015★ 2 cited

Small ball probabilities, maximum density and rearrangements

T. Juškevičius, J. D. Lee

We prove that the probability that a sum of independent random variables in $R^{d}$ with bounded densities lies in a ball is maximized by taking uniform distributions on bal…

math.PR2011

Bounds for tail probabilities of martingales using skewness and kurtosis

Vidmantas Bentkus, Tomas Juškevičius

Let $M_n= \fsu X1n$ be a sum of independent random variables such that $X_{k} \leq 1$ , $\E X_k =0$ and $\E X_k^2=\s_k^2$ for all $k$ . Hoeffding 1963, Theorem 3, proved that $$¶{M_n \…