Asymptotic behavior of the homology of random polyominoes

Probability Seminar

Erika Berenice Roldan Roa (Ohio State)

Thursday, October 11, 2018 -
3:15pm to 4:15pm
119 Physics

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.

Last updated: 2019/06/16 - 10:18pm