Transcription of Percolation Theory - MIT
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Percolation Theory - MIT
Percolation Theory Dr. Kim Christensen Blackett Laboratory Imperial College London Prince Consort Road SW7 2BW London United Kingdom October 9, 2002. Aim The aim of the Percolation Theory course is to provide a challenging and stimulating introduction to a selection of topics within modern theoretical condensed matter physics. Percolation Theory is the simplest model displaying a phase transition. The analytic solutions to 1d and mean-field Percolation are presented. While Percolation cannot be solved exactly for intermediate dimensions, the model enables the reader to become familiar with important concepts such as fractals, scaling, and renormalisation group Theory in a very intuitive way.
gently by developing a basic understanding of percolation theory, providing a natural introduction to the concept of scaling and renormalisation group theory. 1.2 Preliminaries Let P(A) denote the probability for an event Aand P(A1 \A2) the joint probability for event A1 and A2. De nition 1 Two events A1 and A2 are independent ,P(A1 \A2) = P(A1 ...
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