---
res:
bibo_abstract:
- We introduce a hierachy of equivalence relations on the set of separated nets
of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞).
Two separated nets are called ϕ-displacement equivalent if, roughly speaking,
there is a bijection between them which, for large radii R, displaces points of
norm at most R by something of order at most ϕ(R). We show that the spectrum of
ϕ-displacement equivalence spans from the established notion of bounded displacement
equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation,
coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between
the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown
to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞.
We further undertake a comparison of our notion of ϕ-displacement equivalence
with previously studied relations on separated nets. Particular attention is given
to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz
equivalence.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Michael
foaf_name: Dymond, Michael
foaf_surname: Dymond
- foaf_Person:
foaf_givenName: Vojtech
foaf_name: Kaluza, Vojtech
foaf_surname: Kaluza
foaf_workInfoHomepage: http://www.librecat.org/personId=21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
orcid: 0000-0002-2512-8698
bibo_doi: 10.1007/s10711-023-00862-3
bibo_volume: 218
dct_date: 2024^xs_gYear
dct_identifier:
- UT:001105681500001
dct_isPartOf:
- http://id.crossref.org/issn/0046-5755
- http://id.crossref.org/issn/1572-9168
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Divergence of separated nets with respect to displacement equivalence@
...