Matthew I. Roberts

activity

20082026

most citedA simple path to asymptotics for the frontier of a branching Brownian motion

66 citations · 129 across the 23 of their papers we have counts for

collaborators

Showing 2021Show all

4 papers · 1 filter

math.PR2021

The probability of unusually large components for critical percolation on random $d$ -regular graphs

Umberto De Ambroggio, Matthew I. Roberts

Let $d \geq 3$ be a fixed integer, $p \in (0, 1)$ , and let $n \geq 1$ be a positive integer such that $d n$ is even. Let $G (n, d, p)$ be a (random) graph on $n$ vertices obtaine…

math.PR2021★ 2 cited

A spatially-dependent fragmentation process

Alice Callegaro, Matthew I. Roberts

We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin recta…

math.PR2021

Genealogy and spatial distribution of the $N$ -particle branching random walk with polynomial tails

Sarah Penington, Matthew I. Roberts, Zsófia Talyigás

The $N$ -particle branching random walk is a discrete time branching particle system with selection. We have $N$ particles located on the real line at all times. At every time step…

math.PR2021

Unusually large components in near-critical Erdős-Rényi graphs via ballot theorems

Umberto De Ambroggio, Matthew I. Roberts

We consider the near-critical Erdős-Rényi random graph $G (n, p)$ and provide a new probabilistic proof of the fact that, when $p$ is of the form $p = p (n) = 1/ n + λ / n^{4/3}$ and $A$ is la…

The probability of unusually large components for critical percolation on random d-regular graphs

A spatially-dependent fragmentation process

Genealogy and spatial distribution of the N-particle branching random walk with polynomial tails

Unusually large components in near-critical Erdős-Rényi graphs via ballot theorems

The probability of unusually large components for critical percolation on random $d$ -regular graphs

Genealogy and spatial distribution of the $N$ -particle branching random walk with polynomial tails