On measure concentration in graph products
Bollobás and Leader [1] showed that among the n-fold products of connected graphs of order k the one with minimal t-boundary is the grid graph. Given any product graph G and a set A of its vertices that contains at least half of V (G), the number of vertices at a distance at least t from A decays (...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2009-12-01
|
| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/18039 |
| id |
doaj-6f9fae041e764823aaaf72e86790164d |
|---|---|
| record_format |
Article |
| spelling |
doaj-6f9fae041e764823aaaf72e86790164d2020-11-25T03:15:07ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2009-12-0150proc. LMS10.15388/LMR.2009.78On measure concentration in graph productsMatas Šileikis 0Institute of Mathematics and Informatics Bollobás and Leader [1] showed that among the n-fold products of connected graphs of order k the one with minimal t-boundary is the grid graph. Given any product graph G and a set A of its vertices that contains at least half of V (G), the number of vertices at a distance at least t from A decays (as t grows) at a rate dominated by P(X1 + . . . + Xn \geq t) where Xi are some simple i.i.d. random variables. Bollobás and Leader used the moment generating function to get an exponentialbound for this probability. We insert a missing factor in the estimate by using a somewhat more subtle technique (cf. [3]). https://www.journals.vu.lt/LMR/article/view/18039graph productdiscrete isoperimetric inequalitiesconcentration of measuresums of independent random variablestail probabilitieslarge deviations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Matas Šileikis |
| spellingShingle |
Matas Šileikis On measure concentration in graph products Lietuvos Matematikos Rinkinys graph product discrete isoperimetric inequalities concentration of measure sums of independent random variables tail probabilities large deviations |
| author_facet |
Matas Šileikis |
| author_sort |
Matas Šileikis |
| title |
On measure concentration in graph products |
| title_short |
On measure concentration in graph products |
| title_full |
On measure concentration in graph products |
| title_fullStr |
On measure concentration in graph products |
| title_full_unstemmed |
On measure concentration in graph products |
| title_sort |
on measure concentration in graph products |
| publisher |
Vilnius University Press |
| series |
Lietuvos Matematikos Rinkinys |
| issn |
0132-2818 2335-898X |
| publishDate |
2009-12-01 |
| description |
Bollobás and Leader [1] showed that among the n-fold products of connected graphs of order k the one with minimal t-boundary is the grid graph. Given any product graph G and a set A of its vertices that contains at least half of V (G), the number of vertices at a distance at least t from A decays (as t grows) at a rate dominated by P(X1 + . . . + Xn \geq t) where Xi are some simple i.i.d. random variables. Bollobás and Leader used the moment generating function to get an exponentialbound for this probability. We insert a missing factor in the estimate by using a somewhat more subtle technique (cf. [3]).
|
| topic |
graph product discrete isoperimetric inequalities concentration of measure sums of independent random variables tail probabilities large deviations |
| url |
https://www.journals.vu.lt/LMR/article/view/18039 |
| work_keys_str_mv |
AT matassileikis onmeasureconcentrationingraphproducts |
| _version_ |
1724640502065659904 |