Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, September 23, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Will Perkins (NYU)

Forgetfulness of Balls and Bins

Consider two probability distributions on random graphs. In the first we add M random edges. In the second we plant a Hamiltonian cycle, then add (M-n) random edges on top. How large must M be for the two distributions to be statistically indistinguishable? Somewhat surprisingly the distributions are distinguishable for M as high as n^{3/2}, far higher than the threshold for the appearance of Hamiltonian cycles in the random graph. We look at a pure probability model of this phenomenon: if we plant k balls in some arrangement in n labeled bins, how many balls must we throw at random on top to 'forget' the initial planting? We give the exact threshold and total variation limit for any given initial planting. The case of unlabeled bins raises some questions about the concentration of sums of lognormal random variables.

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