Exotic trees.

  title={Exotic trees.},
  author={Zdzislaw Burda and Jenny Erdmann and Bengt Petersson and Marc Wattenberg},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={67 2 Pt 2},
We discuss the scaling properties of free branched polymers. The scaling behavior of the model is classified by the Hausdorff dimensions for the internal geometry, d(L) and d(H), and for the external one, D(L) and D(H). The dimensions d(H) and D(H) characterize the behavior for long distances, while d(L) and D(L) for short distances. We show that the internal Hausdorff dimension is d(L)=2 for generic and scale-free trees, contrary to d(H), which is known to be equal to 2 for generic trees and… 

Figures from this paper

The statistical geometry of scale-free random trees

The properties of random trees (Galton–Watson trees) with scale-free (power-like) probability distribution of coordinations are investigated in the thermodynamic limit. The scaling form of volume

Ageing of complex networks.

This work quantifies differences between the initial and aged network topologies and study the dynamics of the evolution, and implements two versions of the ageing dynamics based on reshuffling of leaves and the other on reshUFFling of branches.

The effects of degree correlations on network topologies and robustness

It is shown that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.

Polyakov lines in Yang-Mills matrix models

We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations

A Social-Ecological Approach to Studying Variation in Urban Trees and Ecosystem Services in the National Municipal District of Santo Domingo, Dominican Republic

Maintaining a diverse urban forest that provides ecosystem services can promote urban sustainability and resilience to environmental change. Around the world, cities have taken to inventorying their

A review of black walnut (Juglans nigra L.) ecology and management in Europe

Black walnut (Juglans nigra L.) is a light-demanding, competition-intolerant, and tall forest tree species, introduced in Europe from North America at the beginning of the seventeenth century. It has



An Introduction To Probability Theory And Its Applications

A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.


  • Rev. E62
  • 2000


  • Phys. B270 [FS16]
  • 1986


  • Rep. 195
  • 1990

Combinatorial Enumeration

and M

  • Staudacher, Phys.Lett. B431
  • 1998


  • Phys. B445
  • 1995

Like, for instance, a theoretical physicist performing analytical calculations

    in Phase Transition and Critical Phenomena 19

    • ed. Domb and Lebowitz, Academic Press, New York,
    • 2000


    • Phys. B498
    • 1997