Related papers: Rejoinder: Brownian distance covariance
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
We respond to comments on our paper, titled "Instrumental variable estimation of the causal hazard ratio."
Rejoinder to "A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?" by B.B. McShane and A.J. Wyner [arXiv:1104.4002]
Rejoinder to the discussion by Hino (2025) and Pardo-Fern\'andez (2025) of Chac\'on and Fern\'andez Serrano (2025), a special paper (with discussion) published in Annals of the Institute of Statistical Mathematics.
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
The Brownian separable permuton is a random probability measure on the unit square, which was introduced by Bassino, Bouvel, F\'eray, Gerin, Pierrot (2016) as the scaling limit of the diagram of the uniform separable permutation as size…
We show how recent results of Lieb and Seiringer [math-ph/0412009; Phys. Rev. A 71, 062329 (2005)] can be obtained from repeated use of the monotonicity of relative entropy under partial traces, and explain how to use their approach to…
A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.
This paper has been withdrawn by the author, since some results of the paper have been already obtained in [J.~Lewandowski, Class. Quantum Grav. 9 (1992), no. 10, L147--L151.]
This paper has been withdrawn by the author(s)
We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…
Rejoinder to ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
A comment on the paper "Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3", Few-Body Syst. 41, 185 (2007) [hep-ph/0511291].
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
Introducing the discussion paper by Sz\'{e}kely and Rizzo
We show how to build an immersion coupling of a two-dimensional Brownian motion $(W_1, W_2)$ along with $\binom{n}{2} + n= \tfrac12n(n+1)$ integrals of the form $\int W_1^iW_2^j \circ dW_2$, where $j=1,\ldots,n$ and $i=0, \ldots, n-j$ for…