תקציר
This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓp, and the particular case of the hypercube.
| שפה מקורית | אנגלית |
|---|---|
| עמודים (מ-עד) | 451-494 |
| מספר עמודים | 44 |
| כתב עת | Advances in Mathematics |
| כרך | 189 |
| מספר גיליון | 2 |
| מזהי עצם דיגיטלי (DOIs) | |
| סטטוס פרסום | פורסם - 20 דצמ׳ 2004 |
| פורסם באופן חיצוני | כן |
הערה ביבליוגרפית
Funding Information:·Corresponding author. Fax: +1-425-936-7329. E-mail addresses: mendelma@cs.huji.ac.il (M. Mendel), anaor@microsoft.com (A. Naor). 1Supported in part by a grant from the Israeli Science Foundation (195/02), and by the Landau Center.