@article {IOPORT.05994403,
    author       = {Colman, E.R. and Rodgers, G.J.},
    title        = {The resistance of randomly grown trees.},
    year         = {2011},
    journal      = {Journal of Physics A: Mathematical and Theoretical},
    volume       = {44},
    number       = {50},
    issn         = {1751-8113},
    pages        = {Article ID 505001, 11 p.},
    publisher    = {IOP Publishing, Bristol},
    doi          = {10.1088/1751-8113/44/50/505001},
    abstract     = {Summary: An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability $p$ or two edges with probability $1 - p$. With each edge having a resistance equal to $1\Omega $, the total resistance $R_{n}$ between the root vertex and a busbar connecting all the vertices at the $n$th level is considered. A dynamical system is presented which approximates $R_{n}$, it is shown that the mean value $\langle R_{n}\rangle $ for this system approaches $(1 + p)/(1 - p)$ as $n \rightarrow \infty $, the distribution of $R_{n}$ at large $n$ is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate $R_{n}$; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with $|\langle R_{n}\rangle - (1 + p)/(1 - p)| \sim n^{ - 1/2}$.},
    identifier   = {05994403},
}