B. Letwin

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math.PR2026

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

Brayden Letwin

We confirm the Kannan--LovÃ¡sz--Simonovits conjecture for quadratic forms: if $X \sim I^¼$ 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.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…

The KLS constant is O(log1/4n)

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

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

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

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