7 papers · 1 filter
Coarse equivalence versus bijective coarse equivalence of expander graphs
Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah +2
We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if…
Abstract embeddability ranks
Florent P. Baudier, Christian Rosendal
We describe several ordinal indices that are capable of detecting, according to various metric notions of faithfulness, the embeddability between pairs of Polish spaces. These embe…
No dimension reduction for doubling subsets of when revisited
Florent P. Baudier, Krzysztof Swieçicki, Andrew Swift
We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of for $q>…
Coarse and Lipschitz universality
Florent P. Baudier, Gilles Lancien, Pavlos Motakis +1
In this paper we provide several \emph{metric universality} results. We exhibit for certain classes $\cC$ of metric spaces, families of metric spaces which ha…
Stochastic approximation of lamplighter metrics
Florent P. Baudier, Pavlos Motakis, Thomas Schlumprecht +1
We observe that embeddings into random metrics can be fruitfully used to study the -embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces…
On the bi-Lipschitz geometry of lamplighter graphs
Florent P. Baudier, Pavlos Motakis, Thomas Schlumprecht +1
In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes…