Related papers: Karl Stein (1913-2000)
Jerzy Neyman's life history and some of his contributions to applied statistics are reviewed. In a 1960 article he wrote: ``Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research which, if…
This paper is devoted to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economists and the best generation of probabilists, most of…
We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by Krause arXiv:1803.09431 and Roos arXiv:1907.00405.
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
Professor Alan Selman has been a giant in the field of computational complexity for the past forty years. This article is an appreciation, on the occasion of his retirement, of some of the most lovely concepts and results that Alan has…
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has…
If $\mathbb{Y}$ is a random vector in $\mathbb{R}^{d}$, we denote by $P_{\mathbb{Y}}$ its probability distribution. Consider a random variable $X$ and a $d$-dimensional random vector $\mathbb{Y}$. Inspired by \cite{Pi}, we develop a…
We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…
We review the observational information on the constancy of the fine structure constant alpha. We find that small improvements on the measurement of ^{187}Re lifetime can provide significant progress in exploring the range of variability…
Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…
We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…
There have been major developments in the theory of moduli of varieties in the past decade, essentially settling the construction of moduli spaces of log canonically polarized slc pairs and moduli spaces of K-polystable log Fano pairs.…
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…
In a recent paper, Roland Bacher conjectured three identities concerning Stern's sequence and its twist. In this paper we prove Bacher's conjectures. Possibly of independent interest, we also give a way to compute the Stern value (or…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
These are the lecture notes based on [dD23] for the (upcoming) lecture "T-systems with a special emphasis on sparse moment problems and sparse Positivstellens\"atze" in the summer semester 2024 at the University of Konstanz. The main…
A short biographical note on the life and works of K. Ramachandra, one of the leading mathematicians in the field of analytic number theory in the second half of the twentieth century.
As we approach the centenary of the discovery of quantum statistics in 1924, it is important to revisit Bose's original derivation of Planck's law usually ignored in most standard presentations of Bose-Einstein statistics. It introduced not…
We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related…