## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

1-30-2009

#### Abstract

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds, and the shortest, the longest, and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.

#### Recommended Citation

Janssen, H., & Stenull, O. (2009). Distribution Functions in Percolation Problems. Retrieved from http://repository.upenn.edu/physics_papers/77

**Date Posted:** 06 January 2011

This document has been peer reviewed.

## Comments

Suggested Citation:

Janssen, H. and O. Stenull. (2009). "Distribution functions in percolation problems."

Physical Review E.79, 011128.© 2009 The American Physical Society

http://dx.doi.org/10.1103/PhysRevE.79.011128