4 papers · 1 filter
Random growth on a Ramanujan graph
Janko Boehm, Michael Joswig, Lars Kastner +1
The behavior of a certain random growth process is analyzed on arbitrary regular and non-regular graphs. Our argument is based on the Expander Mixing Lemma, which entails that the…
Randomized construction of complexes with large diameter
Francisco Criado, Andrew Newman
We consider the question of the largest possible combinatorial diameter among -dimensional simplicial complexes on vertices, denoted . Using a probabilistic c…
The worst way to collapse a simplex
Davide Lofano, Andrew Newman
In general a contractible complex need not be collapsible. Moreover, there exist complexes which are collapsible but even so admit a collapsing sequence where one "gets stuck", tha…
On the complexity of random polytopes
Andrew Newman
There are (at least) two reasons to study random polytopes. The first is to understand the combinatorics and geometry of random polytopes especially as compared to other classes of…