Expectation and variance of self-assembled graph structures

Abstract

Understanding how nanostructures are self-assembled into more complex forms is a crucial component of nanotechnology that shall lead towards understanding other processes and structures in nature. In this paper we use a model of self-assembly using flexible junction molecules and describe how it can in some static conditions be used to predict the outcome of a graph self-assembly. Using probabilistic methods, we show the expectation and the variance of the number of self-assembled cycles, K 3, and discuss generalization of these results for C n. We tie this analysis to previously observed experimental results. © Springer-Verlag Berlin Heidelberg 2006.