Ashwin Sah

activity

20182026

most citedDiagonal Ramsey via effective quasirandomness

6 citations · 11 across the 17 of their papers we have counts for

collaborators

Showing 2023Show all

4 papers · 1 filter

math.NT2023

Improved bounds for five-term arithmetic progressions

James Leng, Ashwin Sah, Mehtaab Sawhney

Let $r_{5} (N)$ be the largest cardinality of a set in ${1, \dots, N}$ which does not contain $5$ elements in arithmetic progression. Then there exists a constant $c \in (0, 1)$ such t…

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…

math.NT2023★ 2 cited

Effective bounds for Roth's theorem with shifted square common difference

Sarah Peluse, Ashwin Sah, Mehtaab Sawhney

Let $S$ be a subset of ${1, \dots, N}$ avoiding the nontrivial progressions $x, x + y^{2} - 1, x + 2 (y^{2} - 1)$ . We prove that $∣ S ∣ ≪ N / lo g_{m} N$ , where $lo g_{m}$ is the $m$ -fold iterated…