Irreducibility and spectral radius of random bipartite tournament matrices
Xinhai Liu, Tan Shang-wang · Zhongguo Shiyou Daxue xuebao. Ziran kexue ban · 2006
Spectral radius of random bipartite tournament matrices was discussed.Set a=12,the following conclusions were obtained.(1)Let m≥n and lim)n→∞m~2a~n=0.Then almost all m×n bipartite tournament matrices are irreducible.(2)Let c_1,c_2 be any positive constants and 1≤c_1≤mn≤c_2.Then for any positive constant e0 and sufficiently large n,the spectral radius ρ(M_(m,n)) of almost all m×n bipartite tournament matrices M_(m,n) satisfy a(1-e)mn-1n≤ρ(M_(m,n))≤a(1+e)mn-1m.