On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs

Assaf Naor

Research output: Contribution to journalArticle

Abstract

We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon-Roichman random Cayley graphs.

Original languageEnglish (US)
Pages (from-to)623-634
Number of pages12
JournalCombinatorics Probability and Computing
Volume21
Issue number4
DOIs
StatePublished - Jul 2012

Fingerprint

Isoperimetry
Banach spaces
Banach space
Cayley Graph
Adjacency Matrix
Normed Space
Graph in graph theory
Random Graphs
Deduce
Norm

ASJC Scopus subject areas

  • Applied Mathematics
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Statistics and Probability

Cite this

On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs. / Naor, Assaf.

In: Combinatorics Probability and Computing, Vol. 21, No. 4, 07.2012, p. 623-634.

Research output: Contribution to journalArticle

@article{45fa9879584d44f1b77e135af4ae3492,
title = "On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs",
abstract = "We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon-Roichman random Cayley graphs.",
author = "Assaf Naor",
year = "2012",
month = "7",
doi = "10.1017/S0963548311000757",
language = "English (US)",
volume = "21",
pages = "623--634",
journal = "Combinatorics Probability and Computing",
issn = "0963-5483",
publisher = "Cambridge University Press",
number = "4",

}

TY - JOUR

T1 - On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs

AU - Naor, Assaf

PY - 2012/7

Y1 - 2012/7

N2 - We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon-Roichman random Cayley graphs.

AB - We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon-Roichman random Cayley graphs.

UR - http://www.scopus.com/inward/record.url?scp=84861963147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861963147&partnerID=8YFLogxK

U2 - 10.1017/S0963548311000757

DO - 10.1017/S0963548311000757

M3 - Article

VL - 21

SP - 623

EP - 634

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 4

ER -