In this talk, I will illustrate two recent results of our group concerning the statistical physics of branched polymers. In the first part, I will present a graph theoretical approach to the configurational statistics of random tree-like objects, which is based on Prüfer labelling. The method, in particular, provides: (i) direct access to the exact configurational entropy as a function of the tree composition, (ii) computable exact expressions for partition functions and important experimental observables for tree ensembles with controlled branching activity and (iii) an efficient sampling scheme for corresponding tree configurations and arbitrary static properties. Then, in the second part, I will introduce a field-theoretic framework for branched polymers with excluded volume interactions. By solving the corresponding partition function by mean-field methods, I will show that the theory is in semi-quantitative agreement with Monte-Carlo computer simulations.
https://indico.ijs.si/event/2878/