Mathematics Colloquia and Seminars

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In this talk we will introduce the random process of independent edge percolation on the $n$ dimensional discrete cube (a.k.a. the hypercube) and state some of the early results related to this process. A biological application of these results to the evolution of species will be discussed as time allows.

The $n$ dimensional cube can be described as the graph with vertex set corresponding to the set of binary strings of length $n$ and edge set corresponding to those pairs of binary strings that differ in exactly one coordinate. The hypercube can be used as a model for the space of genetic sequences of length $n$. The hypercube has a good edge set because two genotypes are adjacent in the hypercube exactly when one can be obtained from the other by a single mutation. Independent edge percolation chooses a random subset of the edge set. This random subset could correspond to those mutations that a sequence actually underwent in biological evolution.