2022/12/10 by Tianxiang Ren, Ren, Tianxiang, Jinwen Wu +1
Mathematics · Physics and Astronomy · Computer Science · #Stochastic processes and statistical mechanics #Complex Network Analysis Techniques #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2212.05233
Consider a rooted N-ary tree. For every vertex of this tree, we atttach an i.i.d. Bernoulli random variable. A path is called open if all the random variables that are assigned on the path are 1. We consider limiting behaviors for the number of open paths from the root to leaves and the longest open path. In addition, when all fitness values are i.i.d. continuous random variables, some asymptotic properties of the longest increasing path are proved.