R. Latala

activity

19992025

most citedExponential and moment inequalities for U-statistics

167 citations · 890 across the 42 of their papers we have counts for

collaborators

Showing 2015Show all

4 papers · 1 filter

math.PR2015★ 58 cited

Royen's proof of the Gaussian correlation inequality

Rafał Latała, Dariusz Matlak

We present in detail Thomas Royen's proof of the Gaussian correlation inequality which states that $μ (K \cap L) \geq μ (K) μ (L)$ for any centered Gaussian measure $μ$ on $R^{d}$ and symm…

math.PR2015★ 13 cited

Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails

Konrad Kolesko, Rafał Latała

We derive two-sided estimates for random multilinear forms (random chaoses) generated by independent symmetric random variables with logarithmically concave tails. Estimates are ex…

math.PR2015

Maximal inequalities for centered norms of sums of independent random vectors

Rafał Latała

Let $X_{1}, X_{2}, \dots, X_{n}$ be independent random variables and $S_{k} = \sum_{i = 1}^{k} X_{i}$ . We show that for any constants $a_{k}$ , \[ \Pr(\max_{1\leq k\leq n}||S_{k}|-a_{k}|>11t)\leq 30 \m…

math.PR2015★ 6 cited

Weak and strong moments of l_r-norms of log-concave vectors

Rafał Latała, Marta Strzelecka

We show that for $p \geq 1$ and $r \geq 1$ the $p$ -th moment of the $l_{r}$ -norm of a log-concave random vector is comparable to the sum of the first moment and the weak $p$ -th moment…