Christoph Koch

activity

20142024

most citedBootstrap percolation on geometric inhomogeneous random graphs

19 citations · 44 across the 12 of their papers we have counts for

collaborators

14 papers

math.PR2024

Bootstrap Percolation on the Binomial Random $k$ -uniform Hypergraph

Mihyun Kang, Christoph Koch, Tamás Makai

We investigate the behaviour of $r$ -neighbourhood bootstrap percolation on the binomial $k$ -uniform random hypergraph $H_{k} (n, p)$ for given integers $k \geq 2$ and $r \geq 2$ . In $r$ -…

math.CO2020

Deviation probabilities for arithmetic progressions and irregular discrete structures

Simon Griffiths, Christoph Koch, Matheus Secco

Let the random variable $X := e (H [B])$ count the number of edges of a hypergraph $H$ induced by a random $m$ -element subset $B$ of its vertex set. Focussing…

math.PR2019

Bivariate fluctuations for the number of arithmetic progressions in random sets

Yacine Barhoumi-Andréani, Christoph Koch, Hong Liu

We study arithmetic progressions ${a, a + b, a + 2 b, \dots, a + (ℓ - 1) b}$ , with $ℓ \geq 3$ , in random subsets of the initial segment of natural numbers $[n] := {1, 2, \dots, n}$ . Given $…

math.CO2018

The size of the giant component in random hypergraphs: a short proof

Oliver Cooley, Mihyun Kang, Christoph Koch

We consider connected components in $k$ -uniform hypergraphs for the following notion of connectedness: given integers $k \geq 2$ and $1 \leq j \leq k - 1$ , two $j$ -sets (of vertices) lie…

math.CO2017★ 2 cited

Finding tight Hamilton cycles in random hypergraphs faster

Peter Allen, Christoph Koch, Olaf Parczyk +1

In an $r$ -uniform hypergraph on $n$ vertices a tight Hamilton cycle consists of $n$ edges such that there exists a cyclic ordering of the vertices where the edges correspond to con…

math.CO2017★ 2 cited

Bootstrap percolation in random $k$ -uniform hypergraphs