Mehtaab Sawhney

activity

20242026

collaborators

Showing math.PRShow all

10 papers · 1 filter

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.PR2025

On random matrices with large corank

Zach Hunter, Matthew Kwan, Lisa Sauermann +1

Let $1 \leq k \leq n$ and $M$ be a random $n \times n$ matrix with independent uniformly random ${\pm 1}$ -entries. We show that there exists an absolute constant $c > 0$ such that \[\…

math.PR2025

Parities in random Latin squares

Matthew Kwan, Kalina Petrova, Mehtaab Sawhney

In a Latin square, every row can be interpreted as a permutation, and therefore has a parity (even or odd). We prove that in a uniformly random $n \times n$ Latin square, the $n$ ro…

math.PR2025

Convergent points for random power series on the unit circle

Marcus Michelen, Mehtaab Sawhney

Consider a random power series of the form $P (z) = \sum_{n \geq 1} ε_{n} a_{n} z^{n}$ where $a_{n} \in C$ are deterministic and $ε_{n}$ are chosen independently…

math.PR2025

The limiting spectral law for sparse iid matrices

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

Let $A$ be an $n \times n$ matrix with iid entries where $A_{ij} \sim Ber (p)$ is a Bernoulli random variable with parameter $p = d / n$ . We show that the empirical measure of…

math.PR2025

On the Spielman-Teng Conjecture

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

Let $M$ be an $n \times n$ matrix with iid subgaussian entries with mean $0$ and variance $1$ and let $I ¨ _{n} (M)$ denote the least singular value of $M$ . We prove that \[\mathbb{P}\bi…

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

On random matrices with large corank

Parities in random Latin squares

Convergent points for random power series on the unit circle

The limiting spectral law for sparse iid matrices

On the Spielman-Teng Conjecture

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