D. Dzindzalieta

activity

20112019

most citedA tight Gaussian bound for weighted sums of Rademacher random variables

26 citations · 35 across the 4 of their papers we have counts for

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5 papers · 1 filter

math.PR2019

A non-uniform Littlewood-Offord inequality

Dainius Dzindzalieta, Tomas Juškevičius

Consider a sum $S_{n} = v_{i} ε_{1} + \dots + v_{n} ε_{n}$ , where $(v_{i})_{i = 1}^{n}$ are non-zero vectors in $R^{d}$ and $(ε_{i})_{i = 1}^{n}$ are independent Ra…

math.PR2013★ 26 cited

A tight Gaussian bound for weighted sums of Rademacher random variables

Vidmantas Kastytis Bentkus, Dainius Dzindzalieta

Let $ε_{1}, \dots, ε_{n}$ be independent identically distributed Rademacher random variables, that is $P {ε_{i} = \pm 1} = 1/2$ . Let $S_n=a_1\varepsilon…

math.PR2013★ 1 cited

Random walks maximizing the probability to visit an interval

Dainius Dzindzalieta

We consider random walks, say $W_{n} = (M_{0}, M_{1}, \dots, M_{n})$ , of length $n$ starting at 0 and based on the martingale sequence $M_{k}$ with differences $X_{m} = M_{m} - M_{m - 1}$ . Assuming that…

math.PR2012★ 1 cited

Extremal Lipschitz functions in the deviation inequalities from the mean

Dainius Dzindzalieta

We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}μ\{f-\E_μ f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$…

math.PR2011★ 7 cited

Optimal Probability Inequalities for Random Walks related to Problems in Extremal Combinatorics

Dainius Dzindzalieta, Matas Šileikis, Tomas Juškevičius

Let S_n=X_1+...+X_n be a sum of independent symmetric random variables such that |X_{i}|\leq 1. Denote by W_n=ε_{1}+...+ε_{n} a sum of independent random variables such that \prob{…