Probability Seminar
Thursday, October 11, 2018, 3:15pm, 119 Physics
Erika Berenice Roldan Roa (Ohio State)
Asymptotic behavior of the homology of random polyominoes
Abstract:- In this talk we study the rate of growth of the expectation of the
number of holes (the rank of the first homology group) in a polyomino
with uniform and percolation distributions. We prove the existence of
linear bounds for the expected number of holes of a polyomino with
respect to both the uniform and percolation distributions.
Furthermore, we exhibit particular constants for the upper and lower
bounds in the uniform distribution case. This results can be extend,
using the same techniques, to other polyforms and higher dimensions. [video]
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