ملخص
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.
| اللغة الأصلية | الإنجليزيّة |
|---|---|
| الصفحات (من إلى) | 451-494 |
| عدد الصفحات | 44 |
| دورية | Advances in Mathematics |
| مستوى الصوت | 189 |
| رقم الإصدار | 2 |
| المعرِّفات الرقمية للأشياء | |
| حالة النشر | نُشِر - 20 ديسمبر 2004 |
| منشور خارجيًا | نعم |
ملاحظة ببليوغرافية
Funding Information:·Corresponding author. Fax: +1-425-936-7329. E-mail addresses: [email protected] (M. Mendel), [email protected] (A. Naor). 1Supported in part by a grant from the Israeli Science Foundation (195/02), and by the Landau Center.