Marcelo Campos

activity

20182023

most citedThe singularity probability of a random symmetric matrix is exponentially small

1 citations · 2 across the 5 of their papers we have counts for

collaborators

10 papers

math.CO2023

An exponential improvement for diagonal Ramsey

Marcelo Campos, Simon Griffiths, Robert Morris +1

The Ramsey number $R (k)$ is the minimum $n \in N$ such that every red-blue colouring of the edges of the complete graph $K_{n}$ on $n$ vertices contains a monochromatic copy…

math.CO2022

Counting orientations of random graphs with no directed k-cycles

Marcelo Campos, Maurício Collares, Guilherme Oliveira Mota

For every $k \geq 3$ , we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of le…

math.MG2022

Towards Hadwiger's conjecture via Bourgain Slicing

Marcelo Campos, Peter van Hintum, Robert Morris +1

In 1957, Hadwiger conjectured that every convex body in $R^{d}$ can be covered by $2^{d}$ translates of its interior. For over 60 years, the best known bound was of the form $…

math.PR2022

The least singular value of a random symmetric matrix

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $A$ be a $n \times n$ symmetric matrix with $(A_{i, j})_{i \leq j}$ , independent and identically distributed according to a subgaussian distribution. We show that $$\mathbb{P}(σ…

math.CO2021★ 1 cited

The typical approximate structure of sets with bounded sumset

Marcelo Campos, Matthew Coulson, Oriol Serra +1

Let $A_{1}$ and $A_{2}$ be randomly chosen subsets of the first $n$ integers of cardinalities $s_{2} \geq s_{1} = Ω (s_{2})$ , such that their sumset $A_{1} + A_{2}$ has size $m$ . We show that asympt…

math.PR2021★ 1 cited

The singularity probability of a random symmetric matrix is exponentially small

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $A$ be drawn uniformly at random from the set of all $n \times n$ symmetric matrices with entries in ${- 1, 1}$ . We show that \[ \mathbb{P}( \det(A) = 0 ) \leq e^{-cn},\] where…

math.PR2020

Singularity of random symmetric matrices revisited

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $M_{n}$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_{n}$ is singular is at most $exp (- c (n lo g n)^{1/2})$ , which repre…

math.CO2019

The Typical Structure of Sets with Small Sumset

Marcelo Campos, Maurício Collares, Robert Morris +2

In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we…

math.CO2019

On the singularity of random symmetric matrices

Marcelo Campos, Letícia Mattos, Robert Morris +1

A well-known conjecture states that a random symmetric $n \times n$ matrix with entries in ${- 1, 1}$ is singular with probability $Θ (n^{2} 2^{- n})$ . In this paper we prove…

math.CO2018

On the number of sets with a given doubling constant

Marcelo Soares Campos

We study the number of $s$ -element subsets $J$ of a given abelian group $G$ , such that $∣ J + J ∣ \leq K ∣ J ∣$ . Proving a conjecture of Alon, Balogh, Morris and Samotij, and improving a r…