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math.MG2025
Metric Poincaré inequalities for graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matoušek'…
math.MG2025
Discrete Poincaré inequalities and universal approximators for random graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable al…
math.CO2025
A universal threshold for geometric embeddings of trees
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
A graph is geometrically embeddable into a normed space when there is a mapping such that if and only if , for…