## 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 $2n$ vertices ($n$ vertices in each part) with $n\log n + cn + o(n)$ edges has positive probability of containing a set of $n$ independent edges as $n$ 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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