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Search: authors:"Radosław Adamczak"

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Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Latała we provide a concentration inequality for not necessarily Lipschitz functions \(f:\mathbb {R}^n \rightarrow \mathbb {R}\) with bounded derivatives of higher orders, which holds when the underlying measure satisfies a family of Sobolev type inequalities $$\begin...

\(U\) -Statistics of Ornstein–Uhlenbeck Branching Particle System

We consider a branching particle system consisting of particles moving according to the Ornstein–Uhlenbeck process in \(\mathbb {R}^d\) and undergoing a binary, supercritical branching with a constant rate \(\lambda >0\) . This system is known to fulfill a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem (CLT) has...