Summary of Lecture 17 - Nov . 10 , 2008 Scribe : David Tisza
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چکیده
1 Executive Summary We have continued with a review on the bond percolation and the introduced the coupling of the bond percolation process, then defined the critical phenomenon and the percolation probability. There is a theorem about the percolation probability is a non decreasing function and we bounded it between 1/3 and 2/3 for the two dimensional case. 2 Bond Percolation 2.1 Preliminaries We have defined L = (Z, E) where edges exist between all vertex pairs with distance 1. Let 0 6 p 6 1 and q = 1 − p. Denote each edge in E to be open with probability p and closed with probability q. We consider the following probability space: As sample space we take Ω = ∏
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