Bose, Arup ; Sen, Arnab
(2007)
*On asymptotic properties of the rank of a special random adjacency matrix*
Electronic Communications in Probability, 12
.
pp. 200-205.
ISSN 1083-589X

Full text not available from this repository.

Official URL: http://ecp.ejpecp.org/article/view/1266

Related URL: http://dx.doi.org/10.1214/ECP.v12-1266

## Abstract

Consider the matrix Δ n =(( I(X i +X j >0) )) i,j=1,2,...,n where {X i } are i.i.d.\ and their distribution is continuous and symmetric around 0 . We show that the rank r n of this matrix is equal in distribution to 2∑ n−1 i=1 I(ξ i =1,ξ i+1 =0)+I(ξ n =1) where ξ i ∼ i.i.d. Ber(1,1/2). As a consequence n − √ (r n /n−1/2) is asymptotically normal with mean zero and variance 1/4 . We also show that n −1 r n converges to 1/2 almost surely.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |

ID Code: | 93945 |

Deposited On: | 30 Jun 2012 08:07 |

Last Modified: | 30 Jun 2012 11:19 |

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