Alexander Volberg

activity

20242026

collaborators

8 papers

cs.IT2026

An $m^{2.943}$ Bohnenblust--Hille Bound on the Boolean Cube

Joseph Slote, Chun-Kai Tseng, Alexander Volberg

Let $q_{m} = 2 m / (m + 1)$ and put \[ β_0=\frac{3}{2}+\frac{1}{\log 2}=2.9426950408\ldots, \] where $lo g$ is the natural logarithm. We give a proof scheme showing that, for every $\vareps…

math.CA2026

Polynomial Bohnenblust--Hille bounds for product of cyclic groups

Joseph Slote, Alexander Volberg

Fix an integer $K \geq 2$ , and let $C_{K}^{n} = {(e^{\frac{2 π ij}{K}})_{j = 0}^{K - 1}}^{n}$ be the product of cyclic groups of order $K$ . For a Fourier character $χ_{α}$ , let $s (α)$ be the numbe…

math.AP2026

Tightness of and counterexamples to several quantum estimates

Joseph Slote, Alexander Volberg, Haonan Zhang

We prove here several tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of $d$ -local hamiltonians, 2) Bohnenblust--Hille inequa…

math.PR2026

Small moments of the sensitivity of polynomial threshold functions

Chun-Kai Tseng, Alexander Volberg

In the first version of Chang, Slote, Volberg, and Zhang's paper \cite{BSA_of_PTF}, the authors modify a nice recursive approach due to Kane in \cite{Correct_exponent_for_AS} where…

cs.CC2026

The estimates for Boolean surface area of polynomial threshold functions

Fan Chang, Joseph Slote, Alexander Volberg +2

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work o…

quant-ph2025

Approximating the operator norm of local Hamiltonians via few quantum states

Lars Becker, Joseph Slote, Alexander Volberg +1

Consider a Hermitian operator $A$ acting on a complex Hilbert space of dimension $2^{n}$ . We show that when $A$ has small degree in the Pauli expansion, or in other words, $A$ is a l…

math.NT2024

Fourier growth of degree $2$ polynomials

Lars Becker, Joseph Slote, Alexander Volberg +1

We prove bounds for the absolute sum of all level- $k$ Fourier coefficients for $(- 1)^{p (x)}$ , where polynomial $p : F_{2}^{n} \to F_{2}$ is of degree $1$ or degree $2$ .

math.FA2024

Noncommutative Bohnenblust--Hille Inequality for qudit systems