• Rapid Communication

Spanning trees in two dimensions

S. S. Manna, Deepak Dhar, and S. N. Majumdar
Phys. Rev. A 46, R4471(R) – Published 1 October 1992
PDFExport Citation

Abstract

We describe the results of an analytical and numerical study of the geometrical properties of random spanning trees on a square lattice. We determine exactly the probability distribution of the coordination number at a site on a random spanning tree. We argue that the probability that s sites get disconnected from the tree on deleting a bond at random from the tree varies as s11/8 for large s. The probability that a loop of perimeter l is formed on adding an additional link at random varies as l8/5 for large l. These distributions are also determined numerically in a Monte Carlo simulation on random spanning trees generated by using Broder’s algorithm. The numerical results are in complete agreement with the theoretical predictions.

  • Received 17 June 1992

DOI:https://doi.org/10.1103/PhysRevA.46.R4471

©1992 American Physical Society

Authors & Affiliations

S. S. Manna

  • Department of Mathematics, Yale University, New Haven, Connecticut 06520

Deepak Dhar and S. N. Majumdar

  • Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

References (Subscription Required)

Click to Expand
Issue

Vol. 46, Iss. 8 — October 1992

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×