Metric embeddings of Laakso graphs into Banach spaces
S. J. Dilworth, Denka Kutzarova, Svetozar Stankov

TL;DR
This paper constructs low-distortion metric embeddings of Laakso graphs into non-super-reflexive Banach spaces and $L_1[0,1]$, revealing geometric properties related to reflexivity and embedding distortions.
Contribution
It demonstrates that Laakso graphs can be embedded with arbitrarily small distortion into certain Banach spaces and provides lower bounds for embeddings into $L_1[0,1]$, advancing understanding of metric embedding theory.
Findings
Embeddings of Laakso graphs into non-super-reflexive Banach spaces with distortion less than 2+ε.
Embeddings into $L_1[0,1]$ with distortion 4/3.
Lower bounds of 9/8 and 5/4 for embeddings of $ ext{Laakso}_2$ and $D_2$ into $L_1[0,1]$.
Abstract
Let be Banach space which is not super-reflexive. Then, for each and , we exhibit metric embeddings of the Laakso graph into with distortion less than and into with distortion . The distortion of an embedding of (respectively, the diamond graph ) into is at least (respectively, ).
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Taxonomy
TopicsChronic Myeloid Leukemia Treatments · IgG4-Related and Inflammatory Diseases
