Percolation -201.2.0101

Instructions • You may use any resources you find such as lecture notes, books, the internet. If you use solutions of exercises found in such, you should reference them in your solution. (For example, “in my solution I use a technique from: G. Orwell. Animal Farm. Chapter 5.”.) If you use such resources, you should not copy a solution, but rather understand it and write it up in your own words. • Work in pairs is permitted, but only in pairs, not more. Do not write up the solutions together, but rather after understanding the solution, each of you should write them up on your own. • You may use any theorems proved in class, but any other propositions you wish to use you should prove. • Please write clearly. State your claims and proofs in a mathematical format, with precise notation and correct formalism. • Make sure your ID no. appears on your solutions. • Each exercise is worth 20 points, although the different parts of a specific exercise are not all equal. Extra points will be awarded for original ideas and proofs. • By taking this exam, you agree to these terms, and declare that you will conform to them.