A. Sah

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20242026

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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…

math.PR2025

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…

math.PR2024

Local limit theorem for joint subgraph counts

Ashwin Sah, Mehtaab Sawhney, Daniel G. Zhu

Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the ErdÅs-RÃ©nyi random graph $G (n, p)$ . This…