3 papers
math.MG2026
Approximate Gromov--Hausdorff continuity of magnitude and weighting
Masahiko Yoshinaga
Magnitude gives an effective size of a finite metric space and is now used in several data-analysis settings. For such applications, it is natural to ask how magnitude behaves unde…
math.MG2025
Is magnitude 'generically continuous' for finite metric spaces?
Hirokazu Katsumasa, Emily Roff, Masahiko Yoshinaga
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the m…
math.MG2023
The small-scale limit of magnitude and the one-point property
Emily Roff, Masahiko Yoshinaga
The magnitude of a metric space is a real-valued function whose parameter controls the scale of the metric. A metric space is said to have the one-point property if its magnitude c…