Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 14, 2022.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2022             April 2022              May 2022
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1  2  3  4  5                   1  2    1  2  3  4  5  6  7
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Thursday, April 14, 2022

2:00 pm in Altgeld Hall 347 ,Thursday, April 14, 2022

#### The ant on a rubber rope paradox

###### Ting-Yang Hsiao (UIUC Math )

Abstract: In this talk, we consider a puzzle called "Ant on a rubber rope”. It is a stochastic process on a random growing domain. To be more specific, an ant is at the left endpoint of a rubber band, which is 1 kilometer long and the ant crawls along with the rubber band at a pace having an expected value of 1 centimeter per second. After the first second, the rubber band stretches extra length L such that the expected value of L is 1 kilometer. Repeat the steps above. It seems that there is a high probability that this ant will not achieve the right endpoint of the rubber band. In this talk, however, we prove that the ant will reach the right end in finite time almost surely.