The Threshold for Integer Homology in Random d-Complexes
Let Y ∼ Y d ( n , p ) denote the Bernoulli random d -dimensional simplicial complex. We answer a question of Linial and Meshulam from 2003, showing that the threshold for vanishing of homology H d - 1 ( Y ; Z ) is less than 40 d ( d + 1 ) log n / n . This bound is tight, up to a constant factor whic...
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| Veröffentlicht in: | Discrete & computational geometry 2017-06, Vol.57 (4), p.810-823 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
Y
∼
Y
d
(
n
,
p
)
denote the Bernoulli random
d
-dimensional simplicial complex. We answer a question of Linial and Meshulam from 2003, showing that the threshold for vanishing of homology
H
d
-
1
(
Y
;
Z
)
is less than
40
d
(
d
+
1
)
log
n
/
n
. This bound is tight, up to a constant factor which depends on
d
. |
|---|---|
| ISSN: | 0179-5376 1432-0444 |
| DOI: | 10.1007/s00454-017-9863-1 |