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| Irreducibility and spectral radius of random bipartite tournament matrices |
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LIU Xin-hsi,TAN Shang-wang
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(College o Mathematics and Computational Science in China University o Petroleum，Dongying 2^57061， Shndong Province， China )
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| Abstract: |
| Spectral radius of random bipartite tournament matrices was discussed. Set a = ^， the following conclusions were obtained. (1)Let m!n and limm2an = 0, Then almost Si m 2 n bipartite tournament matricss are irreducible. (2)Let $1，C2 be any positive constants and 1#C1#m#C2. Then for any positive constant e >0 and sufficiently large n，the 1 2 1 n 2 spectral radius (5Mm，?) of almott all m 2 n bipartite tournament matrices Mm，n satisfy <5(1 — e\J mn $ 丄#:(Mm,n) |
| Key words: random bipartite tournament matrix itreducible spectral radius |
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