1-1hit |
Tomonori ANDO Yoshiyuki KABASHIMA Hisanao TAKAHASHI Osamu WATANABE Masaki YAMAMOTO
We study nn random symmetric matrices whose entries above the diagonal are iid random variables each of which takes 1 with probability p and 0 with probability 1-p, for a given density parameter p=α/n for sufficiently large α. For a given such matrix A, we consider a matrix A ' that is obtained by removing some rows and corresponding columns with too many value 1 entries. Then for this A', we show that the largest eigenvalue is asymptotically close to α+1 and its eigenvector is almost parallel to all one vector (1,...,1).