Dan Romik (Weizmann I.)

will speak

Bootstrap percolation and partitions.

Abstract:

For 0 < a < b, let f:[0,1]->[0,1] be the unique decreasing function that satisfies f(x)^a - f(x)^b = x^a - x^b. Then the integral of -log(f(x))/x dx over [0,1] is equal to pi^2/3ab. I will show two applications of this mysterious definite integral: First, to determine the asymptotic behavior of bootstrap percolation, which is a cellular automaton growth model with random initial conditions. Second, to count the number of integer partitions not containing consecutive parts. (joint work with Alexander Holroyd and Thomas Liggett)

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Last update on 20/10/02.