## Analysis and PDE

•  Dimitris Vardakis, MSU
•  Buffon's needle problem for a random planar disk-like Cantor set
•  11/09/2022
•  4:10 PM - 5:00 PM
•  C304 Wells Hall
•  Willie Wai-Yeung Wong (wongwil2@msu.edu)

The Favard length of the planar $1/4$-corner Cantor set is $0$. Estimates exists about the rate with which the Favard length of the previous steps goes to $0$, but the exact rate of decay is unknown. However, if one considers a random construction of the $1/4$-corner Cantor set, things might seem better. In fact, Peres and Solomyak showed that the rate of decay for the average Favard length for the random $1/4$-corner Cantor set is of order exactly $1/n$. We show that the rate of decay for a random disk-like analogue has again order $1/n$. This suggests that any reasonable'' random Cantor set of positive and finite length might decay at the same rate.

## Contact

Department of Mathematics
Michigan State University