Department of

Mathematics


Seminar Calendar
for graduate probability seminar events the year of Sunday, July 3, 2022.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 3, 2022

2:00 pm in zoom: https://illinois.zoom.us/j/84500990503?pwd=Szhhb0xIUktoM2wxQ29xaERmUVpMZz09.,Thursday, February 3, 2022

Robust Mean Estimation

Grigory Terlov (UIUC Math )

Abstract: One of the most fundamental problems of statistics is to estimate the expected value of a random variable given $n$ i.i.d. samples. It is natural to do so by considering the empirical mean, however when one works with heavy-tailed distributions empirical mean would give less than ideal accuracy and confidence intervals for finite $n$ and thus one has to consider other estimators. In the first talk I will elaborate on this problem; present several other estimators such as median-of-means, Catoni’s estimator, and Trimmed median; and prove some basics results about them. My talks will be based on the survey paper by Lugosi and Mendelson https://arxiv.org/abs/1906.04280. Here is a zoom link: https://illinois.zoom.us/j/84500990503?pwd=Szhhb0xIUktoM2wxQ29xaERmUVpMZz09.

Thursday, March 31, 2022

2:00 pm in Altgeld Hall 347 ,Thursday, March 31, 2022

An introduction to Pirogov-Sinai Theory

Bob Krueger (UIUC MATH)

Abstract: I will introduce a few spin models on lattices and discuss the usual polymer models. Then I will describe the polymer model at the basis of Pirogov-Sinai Theory. I hope to get to a recent result of Helmuth, Perkins, and Regts which uses Pirogov-Sinai Theory to efficiently sample from these spin models at low temperatures. I assume no knowledge of statistical physics.

Thursday, April 7, 2022

2:00 pm in Altgeld Hall 347 ,Thursday, April 7, 2022

An introduction to Pirogov-Sinai Theory

Bob Krueger (UIUC Math )

Abstract: I will introduce a few spin models on lattices and discuss the usual polymer models. Then I will describe the polymer model at the basis of Pirogov-Sinai Theory. I hope to get to a recent result of Helmuth, Perkins, and Regts which uses Pirogov-Sinai Theory to efficiently sample from these spin models at low temperatures. I assume no knowledge of statistical physics.

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.