相关论文: Parametrized Kantorovich-Rubinstein theorem and ap…
Tchakaloff's Theorem establishes the existence of a quadrature rule of prescribed degree relative to a positive, compactly supported measure that is absolutely continuous with respect to Lebesgue measure on $\mathbb{R}^{d}$. Subsequent…
An easy consequence of Kantorovich-Rubinstein duality is the following: if $f:[0,1]^d \rightarrow \infty$ is Lipschitz and $\left\{x_1, \dots, x_N \right\} \subset [0,1]^d$, then $$ \left| \int_{[0,1]^d} f(x) dx - \frac{1}{N}…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation…
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as a mathematical problem with complementarity constraints in…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
We present an orthogonal expansion for real, function-regulated, second-order random measures over $\mathbb{R}^{d}$ with measure covariance. Such a expansion, which can be seen as a Karhunen-Lo\`eve decomposition, consists in a series of…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
It is shown that the Marcinkiewicz-Zygmund strong law of large numbers holds for pairwise independent identically distributed random variables. It is proved that if $X_{1}, X_{2}, \ldots$ are pairwise independent identically distributed…
We develop Wasserstein-based hypothesis tests for empirical-measure convergence in stationary dependent sequences. For a known candidate invariant measure, $\mu$, we study the statistic $T_n=\sqrt{n}\,W_1(\hat\mu_n,\mu)$ and establish…
The main results of this note extend a theorem of Kesten for symmetric random walks on discrete groups to group extensions of topological Markov chains. In contrast to the result in probability theory, there is a notable asymmetry in the…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two…
The main object of this paper is to improve some of the known estimates for classical Kantorovich operators. A quantitative Voronovskaya-type result in terms of second moduli of continuity which improves some previous results is obtained.…
We extend Painlev\'e's determinateness theorem from the theory of ordinary differential equations in the complex domain allowing more general 'multiple-valued' Cauchy's problems. We study $C^0-$continuability (near singularities) of…
Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to…
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…
This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…