Julian Sahasrabudhe

collaborators

3 papers

math.PR2024

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 $σ_{n} (M)$ denote the least singular value of $M$ . We prove that \[\mathbb{P}\big…

math.PR2023

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.PR2023

The sparse circular law, revisited

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

Let $A_{n}$ be an $n \times n$ matrix with iid entries distributed as Bernoulli random variables with parameter $p = p_{n}$ . Rudelson and Tikhomirov, in a beautiful and celebrated paper…