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Yonathan Stone

Publications and source records attributed to Yonathan Stone.

6 recordsLinked to original sources
arXiv2024

Sharpening the gap between $L^{1}$ and $L^{2}$ norms

We refine the classical Cauchy--Schwartz inequality $\|X\|_{1} \leq \|X\|_{2}$ by demonstrating that for any $p$ and $q$ with $q>p>2$, there exists a constant $C=C(p,q)$ such that $\|X\|_1 \leq 1 - C \Big{(}\|X\|_p^p - 1\Big{)}^{\frac{q-2}{q-p}}\Big{(}\|X\|_q^q - 1\Big{)}^{\frac{2-p}{q-p}}$ holds true for all Borel measurable random variables $X$ with $\|X\|_{2}=1$ and $\|X\|_{p}<\infty$. We illustrate two applications of this result: one for biased Rademacher sums and another for exponential sums.

math.PR↗
arXiv2022

Alexander Ostrowski's "On Dirichlet Series and Algebraic Differential Equations"

This is an English translation of Ostrowski's article "\"Uber Dirichletsche Reihen und algebraische Differentialgleichungen" published German in Math. Zeit. vol. 8, 1920, pp. 241-298. In this article, Ostrowski proves a conjecture of Hilbert that the two variable function $\zeta(x,s)=\sum_{n\ge 1} \frac{x^n}{n^s}$ cannot be written as a composition of analytic functions of one variable and algebraic functions of any number of variables.

math.HO↗
arXiv2022

The KKL inequality and Rademacher type 2

We show that a vector-valued Kahn--Kalai--Linial inequality holds in every Banach space of Rademacher type 2. We also show that for any nondecreasing function $h\geq 0$ with $0<\int_{1}^{\infty}\frac{h(t)}{t^{2}}\mathrm{dt}<\infty$ we have the inequality \begin{align*} \|f - \mathbb{E}f\|_2 \leq 12 \, T_{2}(X) \left(\int_{1}^{\infty}\frac{h(t)}{t^{2}} \mathrm{dt} \right)^{1/2} \, \left(\sum_{j=1}^n \frac{\|D_j f\|^{2}_2}{h\left( \log \frac{\|D_j f\|_2}{\|D_j f\|_1} \right)}\right)^{1/2} \end{align*} for all $f :\{-1,1\}^{n} \to X$ and all $n\geq 1$, where $X$ is a normed space and $T_{2}(X)$ is the associated type 2 constant.

math.PR↗
arXiv2020

Nikolai Chebotaryov's "Problems in Modern Galois Theory"

This is an English translation of Nikolai Chebotaryov's paper "Die Probleme der modernen Galoisschen Theorie" from 1932. An excerpt from this paper was given as a lecture at the International Congress of Mathematicians in Z\"urich in 1932. With the lecture being given to commememorate the centennial of Evariste Galois' death, the paper is a broad survey of various contemporary problems in Galois Theory the author found represented the culminations of work done by Galois and his successors.

math.HO↗