Spectral Analysis of Random Sparse Matrices

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概要

• 論文の詳細を見る

• We study n×n 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).

• 2011-06-01

著者

• YAMAMOTO Masaki

  Department of Chemistry, Faculty of Science, Okayama University

• Watanabe Osamu

  Dept. Of Math. And Comp. Sciences Tokyo Institute Of Technology

• ANDO Tomonori

  Canon Inc.

• KABASHIMA Yoshiyuki

  Dept. of Comp. Intelligence and Systems Science, Tokyo Institute of Technology

• TAKAHASHI Hisanao

  Tokai University and Tokyo Institute of Technology

• Watanabe Osamu

  Dept. Computer Science Tokyo Institute Of Technology

• Kabashima Yoshiyuki

  Dept. Of Comp. Intelligence And Systems Science Tokyo Institute Of Technology

• Yamamoto Masaki

  Department Of Cardiovascular Surgery Chiba Cardiovascular Center

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