Related papers: A combinatorial approach to small ball inequalitie…
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth Banach spaces. This is used to obtain optimum bounds of the…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to…
We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot)…
We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimension-free and depend on the…
We analyze the quality of the gaussian approximation to linear combinations of n independent, identically-distributed random variables with finite fourth moments. It turns out that there exist universal, simple linear combinations that…
Handball has received growing interest during the last years, including academic research for many different aspects of the sport. On the other hand modelling the outcome of the game has attracted less interest mainly because of the…
This is a comprehensive set of notes on the ArXiV paper math.CA/0609815 by Dmitry Bilyk and the author. The focus of that paper is a new inequality for sums of hyperbolic Haar functions in three variables, extending a famous result of J…
Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…
We continue the research of Lata{\l}a on improving estimates of $p$-th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \leq 4$ and present a combinatorial approach for even…
We show a deviation inequality for U-statistics of independent data taking values in a separable Banach space which satisfies some smoothness assumptions. We then provide applications to rates in the law of large numbers for U-statistics, a…
While small ball, or lower tail, asymptotic for Gaussian measures generated by solutions of stochastic ordinary differential equations is relatively well understood, a lot less is known in the case of stochastic partial differential…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
\noindent We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. We prove a Berry-Esseen bound…
The l1-regularization is very popular in high dimensional statistics -- it changes a combinatorial problem of choosing which subset of the parameter are zero, into a simple continuous optimization. Using a continuous prior concentrated near…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.
In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.