Related papers: Concentration Inequalities in Riesz Spaces

We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and…

We introduce the notion of unbounded locally solid Riesz spaces, and investigate its fundamental properties.

We present a generalization of the Radon-Riesz property to sequences of continuous functions with values in uniformly convex and uniformly smooth Banach spaces.

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary density conditions for coherent frames and Riesz sequences for…

This preprint concerns Banach spaces of functions converging at infinity. In particular, spaces of continuous functions, Lebesgue spaces and sequence spaces. In each framework we show versions of Riesz's representation theorem.

We derive concentration inequalities for empirical means $\frac{1}{t} \int_0^t f(X_s) ds$ where $X_s$ is an irreducible Markov jump process on a finite state space and $f$ some observable. Using a Feynman-Kac semigroup we first derive a…

Formulas for calculating the Riesz function, introduced by Marcel Riesz in connection with the Riemann hypothesis, are derived; and the behavior of the Riesz function is discussed.

We establish upper bounds for moments of zeta sums using results on shifted moments of the Riemann zeta function under the Riemann hypothesis.

For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities, transportation inequalities…

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…

In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…

We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies $\Gamma$-converge in the weak-$*$ topology to the Riesz functional…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

We introduce a new type of norm for ordered vector spaces majorized by a proper (convex) cone that generalizes the notions of order unit norm and base norm. Then we give sufficient conditions to ensure its completeness. In the case of…

For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $\phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $\displaystyle \phi(\lambda_{1}) \mu(\{x \in \Omega : f(x) \geq…

We show that for any metric probability space $(M,d,\mu)$ with a subgaussian constant $\sigma^2(\mu)$ and any set $A \subset M$ we have $\sigma^2(\mu_A) \leq c \log\left(e/\mu(A)\right)\,\sigma^2(\mu)$, where $\mu_A$ is a restriction of…

In this paper, we establish a class of Stein-Weiss type inequality with partial variable weight functions on the upper half space using a weighted Hardy type inequality. Overcoming the impact of weighted functions, the existence of extremal…

In this paper we find the condition on function $\omega$ and weight $v$ which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces ${\mathcal…