Uniform recursive trees: Branching structure and simple random downward walk

作者：Su C^*; Feng QQ; Hu ZS

来源：Journal of Mathematical Analysis and Applications, 2006, 315(1): 225-243.

DOI：10.1016/j.jmaa.2005.05.004

• uniform recursive tree
• branch
• SRDW
• walk length
• asymptotic behavior

As models for spread of epidemics, family trees, etc., various authors have used a random tree called the uniform recursive tree. Its branching structure and the length of simple random downward walk (SRDW) on it are investigated in this paper. On the uniform recursive tree of size n, we first give the distribution law of zeta(n,m) the number of m-branches, whose asymptotic distribution is the Poisson distribution with parameter lambda = 1/m. We also give the joint distribution of the numbers of various branches and their covariance matrix. On L-n the walk length of SRDW, we first give the exact expression of P(L-n = 2). Finally, the asymptotic behavior of L-n is given.

• 出版日期2006-3-1
• 单位中国科学技术大学