Mehtaab Sawhney

activity

20152026

most citedThe number of independent sets in an irregular graph

14 citations · 74 across the 75 of their papers we have counts for

collaborators

Showing 2024Show all

12 papers · 1 filter

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 Erdős-Rényi random graph $G (n, p)$ . This li…

math.NT2024

New bounds for the Furstenberg-Sárközy theorem

Ben Green, Mehtaab Sawhney

Suppose that $A \subset {1, \dots, N}$ has no two elements differing by a square. Then $∣ A ∣ ≪ N e^{- c l o g N}$ .

math.PR2024

Hitting time mixing for the random transposition walk

Vishesh Jain, Mehtaab Sawhney

Consider shuffling a deck of $n$ cards, labeled $1$ through $n$ , as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uni…

math.NT2024

Primes of the form $p^{2} + n q^{2}$

Ben Green, Mehtaab Sawhney

Suppose that $n$ is $0$ or $4$ modulo $6$ . We show that there are infinitely many primes of the form $p^{2} + n q^{2}$ with both $p$ and $q$ prime, and obtain an asymptotic for their nu…

math.NT2024★ 1 cited

Vinogradov's theorem for primes with restricted digits

James Leng, Mehtaab Sawhney

Let $g$ be sufficiently large, $b \in {0, \dots, g - 1}$ , and $S_{b}$ be the set of integers with no digit equal to $b$ in their base $g$ expansion. We prove that every suffic…

math.PR2024

Free Energy Universality of Spherical Spin Glasses

Mehtaab Sawhney, Mark Sellke

We prove the free energy and ground state energy of spherical spin glasses are universal under the minimal moment assumptions. Previously such universality was known only for Ising…

math.CO2024

An explicit economical additive basis

Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1

We present an explicit subset $A \subseteq N = {0, 1, \dots}$ such that $A + A = N$ and for all $ε > 0$ , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…

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.NT2024

On further questions regarding unit fractions

Yang P. Liu, Mehtaab Sawhney

We prove that a subset $A \subseteq [1, N]$ with \[\sum_{n\in A}\frac{1}{n} \ge (\log N)^{4/5 + o(1)}\] contains a subset $B$ such that \[\sum_{n\in B} \frac{1}{n} = 1.\] Our techni…

math.CO2024

Improved Bounds for Szemerédi's Theorem

James Leng, Ashwin Sah, Mehtaab Sawhney

Let $r_{k} (N)$ denote the size of the largest subset of $[N] = {1, \dots, N}$ with no $k$ -term arithmetic progression. We show that for $k \geq 5$ , there exists $c_{k} > 0$ such that \[r_…

math.CO2024

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm

James Leng, Ashwin Sah, Mehtaab Sawhney

We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input rece…

math.CO2024

A central limit theorem for the matching number of a sparse random graph

Margalit Glasgow, Matthew Kwan, Ashwin Sah +1

In 1981, Karp and Sipser proved a law of large numbers for the matching number of a sparse Erdős-Rényi random graph, in an influential paper pioneering the so-called differential e…

Local limit theorem for joint subgraph counts

New bounds for the Furstenberg-Sárközy theorem

Hitting time mixing for the random transposition walk

Primes of the form p2+nq2

Vinogradov's theorem for primes with restricted digits

Free Energy Universality of Spherical Spin Glasses

An explicit economical additive basis

On the Spielman-Teng Conjecture

On further questions regarding unit fractions

Improved Bounds for Szemerédi's Theorem

Quasipolynomial bounds on the inverse theorem for the Gowers Us+1[N]-norm

A central limit theorem for the matching number of a sparse random graph

Primes of the form $p^{2} + n q^{2}$

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm