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math.MG2026
The microscopic weighting on a metric space
Emily Roff, Simon Willerton
We introduce the microscopic weighting, a canonical signed measure of mass one that can be associated to almost any finite metric space. The microscopic weighting is obtained as th…
math.MG2025
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…
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…