Noise stability of functions with low influences: invariance and optimality (2005)
Mossel, Elchanan, O'Donnell, Ryan, Oleszkiewicz, Krzysztof
In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It...
Small ball probability estimates in terms of width (2005)
Latała, Rafał, Oleszkiewicz, Krzysztof
A certain inequality conjectured by Vershynin is studied. It is proved that for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK)...
Elchanan Mossel, Krzysztof Oleszkiewicz
stability of functions with low influences:
Upper tails for subgraph counts in random graphs (2004)
Svante Janson, Krzysztof Oleszkiewicz, Ruci Ński
Abstract. Let G be a fixed graph and let XG be the number of copies of G contained in the random graph G(n, p). We prove exponential bounds on the upper tail of XG which are best possible up to a...
Power-Bounded Operators and Related Norm Estimates (2004)
Nigel Kalton, Stephen Montgomery-smith, Krzysztof Oleszkiewicz, Yuri Tomilov
We consider whether L = lim sup n!1 nkT 1 implies that the operator T is power bounded. We show that this is so if L < 1=e, but it does not necessarily hold if L = 1=e. As part of our methods, we...
Power-bounded operators and related norm estimates (2002)
Kalton, Nigel, Montgomery-Smith, Stephen, Oleszkiewicz, Krzysztof, Tomilov, Yuri
We consider whether L = limsup_{n to infty} n ||T^{n+1}-T^n|| < infty implies that the operator T is power bounded. We show that this is so if L= 1/e. The constant 1/e is sharp. Finally we describe a...
Harcharras, Asma, Neuwirth, Stefan, Oleszkiewicz, Krzysztof
We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier...
Between Sobolev and Poincar\'e (2000)
Latała, Rafał, Oleszkiewicz, Krzysztof
We establish a family of functional inequalities interpolating between the classical logarithmic Sobolev and Poincar\'e inequalities. We prove that they imply the concentration of measure phenomenon...
Gaussian Measures of Dilatations of Convex Symmetric Sets (1999)
Latała, Rafał, Oleszkiewicz, Krzysztof
We prove that the inequality $\Psi^-1(\mu(tA))\geq t\Psi^-1(\mu(A))$ holds for any centered Gaussian measure $\mu$ on a separable Banach space $F$, any convex, closed, symmetric set $A\subsetF$ and...
Recently Albin constructed an example of a continuous martingale different from the classical Brownian motion but with the same marginal distributions, thus improving on the result of Hamza and...
Concentration of capital--the product form of the Law of Large Numbers in L1
Let X1,X2,... be i.i.d. copies of a non-negative real random variable X having continuous distribution and such that EX(lnX)3
On certain characterization of normal distribution
A conjecture of Bobkov and Houdré (1995), recently proved by Kwapien et al. (1995), stated that if X and Y are symmetric i.i.d. real random variables such that P((X + Y)/[radical sign]2 > t)...