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Percolation and the Random Cluster Model: Combinatorial and Algorithmic Problems

  • Dominic Welsh
Part of the Algorithms and Combinatorics book series (AC, volume 16)

Abstract

In 1961 Harry Frisch, John Hammersley and I [13] carried out what were in those days massive Monte Carlo experiments attempting to determine the critical percolation probabilities of the various standard lattices. The constraints at that time were, as today, machine induced. The programmes were written in machine code on a computer which was the size of a large room with less power than a modern day calculator. Today the situation has radically changed. Several of these critical probabilities which we were trying to estimate are now known exactly. However the problems posed then have been replaced by problems of just as much charm and seeming intractability and it is some of these that I shall address in these lectures.

Keywords

Partition Function Ising Model Critical Probability Jones Polynomial Weight Enumerator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dominic Welsh
    • 1
  1. 1.University of OxfordUK

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