Erdös and Rényi's "On Random Matrices"

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For our weekly research class I had to prepare a presentation of "On random matrices" by Erdös and Rényi. Despite the title, it is essentially about bipartite graphs, proving that a random bipartite graph on vertices ( vertices in each part) with edges has positive probability of containing a set of independent edges as grows infinitely.

The paper is written in an over-concise manner and relies heavily on tricky manipulation of binomial coefficients. I spent several days figuring out all the details, so I thought it would be nice to have the commentary online, should someone ever need help on the paper.
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