Asymptotic behavior of two-terminal series-parallel networks
O. Golinelli
Abstract
This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied probability theory as a model for real networks. The number of networks grows asymptotically like Rn/nalpha, as for some models of statistical physics like self-avoiding walks, lattice animals, meanders, etc. By using a exact recurrence relation, the entropy is numerically estimated at R = 3.5608393095389433(1), and we show that the sub-leading universal exponent alpha is 3/2.
Create a lesson
Related papers
Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field
Ran Luo, Jiahua Tian
Physical limits to stochastic classifiers
Timur Aslyamov, Massimiliano Esposito
Absolute area under a scaled Brownian motion with resetting
Vicenç Méndez, Javier Cristín
Understanding the Mpemba Effect through a Rule of Thumb
Ran Yaacoby
Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component
Mykhailo Hontarenko, Wojciech Tarnowski, Sergey Denisov et al.
Towards synergy between theory and experiments: First-passage processes under resetting with stochastic return protocols
Ashutosh Dubey, Arnab Pal