M. Kahle

activity

20062026

most citedRandom geometric complexes

172 citations · 377 across the 33 of their papers we have counts for

collaborators

Showing 2022Show all

4 papers · 1 filter

math.CO2022

Maximal persistence in random clique complexes

Ayat Ababneh, Matthew Kahle

We study the persistent homology of an Erdős--Rényi random clique complex filtration on $n$ vertices. Here, each edge $e$ appears at a time $p_{e} \in [0, 1]$ chosen uniform randomly…

math.CO2022

On the clique number of noisy random geometric graphs

Matthew Kahle, Minghao Tian, Yusu Wang

Let $G_{n}$ be a random geometric graph, and then for $q, p \in [0, 1)$ we construct a " $(q, p)$ -perturbed noisy random geometric graph" $G_{n}^{q, p}$ where each existing edge in $G_{n}$ is…

math.AT2022★ 1 cited

Asymptotic Betti numbers for hard squares in the homological liquid regime

Hannah Alpert, Matthew Kahle, Robert MacPherson

We study configuration spaces $C (n; p, q)$ of $n$ ordered unit squares in a $p$ by $q$ rectangle. Our goal is to estimate the Betti numbers for large $n$ , $j$ , $p$ , and $q$ . We con…

math.CO2022★ 2 cited

Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering

Benjamin Braun, Kaitlin Bruegge, Matthew Kahle

Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symm…