B. Letwin

collaborators

6 papers

math.MG2026

Strongly log-concave measures and lattices

Brayden Letwin, Victor Reis, Thomas Rothvoss

Let $Λ \subseteq R^{n}$ be a full rank lattice with the property that $det Γ \geq 1$ for all sublattices $Γ \subseteq Λ^{*}$ . We prove that there exists a symmetric random vector…

math.PR2026

The KLS constant is $O (lo g^{1/4} n)$

Brayden Letwin

We confirm the Kannan--Lovász--Simonovits conjecture for quadratic forms: if $X \sim μ$ is an isotropic log-concave random vector in $R^{n}$ , then for any symmetric matrix $…

math.PR2026

On the smallest singular value of the product of random and deterministic matrices

Brayden Letwin, Achintya Raya Polavarapu

Let $A = (a_{ij})$ be an $n \times n$ real-valued random matrix with independent, mean-zero, variance-one entries whose fourth moments are uniformly at most $K$ . Suppose that there ex…

math.MG2026

Dimension-free Gaussian tail estimates for linear functionals on convex bodies

Brayden Letwin, Dan Mikulincer

Let $K \subset R^{n}$ be a centered convex body of volume one. We prove that there exist absolute constants $c, C > 0$ and an orthonormal set of vectors $Θ \subset S^{n - 1}$ wi…

math.PR2026

On the maxima of Littlewood polynomials on $[- 1, 1]$

Brayden Letwin, Mehtaab Sawhney

A Littlewood polynomial is a polynomial of the form \[ f_n(x)=\sum_{k=0}^n \varepsilon_k x^k \] with $ε_{k} \in {- 1, 1}$ . Let $(ε_{k})_{k \geq 0}$ be i.i.d. Rademach…

math.MG2024

A generalization of Grünbaum's inequality

Brayden Letwin, Vladyslav Yaskin

Grünbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of t…

Strongly log-concave measures and lattices

The KLS constant is O(log1/4n)

On the smallest singular value of the product of random and deterministic matrices

Dimension-free Gaussian tail estimates for linear functionals on convex bodies

On the maxima of Littlewood polynomials on [−1,1]

A generalization of Grünbaum's inequality

The KLS constant is $O (lo g^{1/4} n)$

On the maxima of Littlewood polynomials on $[- 1, 1]$