P. Balister

activity

20052025

most citedContinuum percolation with steps in an annulus

18 citations · 78 across the 34 of their papers we have counts for

collaborators

42 papers

math.CO2025

A local limit theorem for the edge counts of random induced subgraphs of a random graph

Paul Balister, Emil Powierski, Alex Scott +1

Consider a `dense' Erdős--Rényi random graph model $G = G_{n, M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M / (2 n)$ is bounded away from 0 and 1. Fix…

math.CO2024★ 2 cited

Upper bounds for multicolour Ramsey numbers

Paul Balister, Béla Bollobás, Marcelo Campos +5

The $r$ -colour Ramsey number $R_{r} (k)$ is the minimum $n \in N$ such that every $r$ -colouring of the edges of the complete graph $K_{n}$ on $n$ vertices contains a monochroma…

math.CO2024

Reconstruction of shredded random matrices

Paul Balister, Gal Kronenberg, Alex Scott +1

A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matr…

math.FA2023

Random Translates in Minkowski Sums

Paul Balister, Bela Bollobas, Imre Leader +1

Suppose that $A$ and $B$ are sets in $R^{d}$ , and we form the sumset of $A$ with $n$ random points of $B$ . Given the volumes of $A$ and $B$ , how should we choose them to min…

math.CO2023★ 1 cited

Counting graphic sequences via integrated random walks

Paul Balister, Serte Donderwinkel, Carla Groenland +2

Given an integer $n$ , let $G (n)$ be the number of integer sequences $n - 1 \geq d_{1} \geq d_{2} \geq \dots \geq d_{n} \geq 0$ that are the degree sequence of some graph. We show that $G(n)=(c+o(1))…

math.CO2022

Erdős covering systems

Paul Balister, Béla Bollobás, Robert Morris +2

A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the foll…