Department of Mathematics

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 (

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.



Department of Mathematics
Michigan State University
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