Related papers: Restricted Khinchine inequality
We compute the best constant in the Khintchine inequality under assumption that the sum of Rademacher random variables is zero.
We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's…
We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ $k$-wise independent Rademacher random variables. We show that an analogue of Khintchine's inequality holds, with a constant $N^{1/2-k/2p}$, when $k$ is even.…
For discrete martingale-difference sequences $d=\{d_1,\ldots,d_n\}$ we consider Khintchine type inequalities, involving certain square function $\mathfrak S (d)$ considered by Chang-Wilson-Wolff in 1982. In particular, we prove…
We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on $\R^n$. This is an application of small ball estimate and Chernoff's…
In this note we prove a weighted version of the Khintchine inequalities.
We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ pairwise independent Rademacher random variables. We establish that an analogue of Khintchine's inequality cannot hold in this setting with a constant that is…
We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is replaced by general symmetric distributions. The proof…
In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…
We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…
Normalized free semi-circular random variables satisfy an upper Khintchine inequality in $L_\infty$. We show that this implies the corresponding upper Khintchine inequality in any noncommutative Banach function space. As applications, we…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let…
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit…
We prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.
We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the…
We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers.…
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…