Department of

Mathematics


Seminar Calendar
for Graduate Probability Seminar events the year of Monday, September 27, 2021.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2021           September 2021          October 2021    
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  1  2  3  4  5  6  7             1  2  3  4                   1  2
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
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 22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
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Thursday, September 23, 2021

2:00 pm in Altgeld Hall 347,Thursday, September 23, 2021

Coupling from the Past 1

Aditya Suresh Gopalan (UIUC ISE )

Abstract: Abstract: The Coupling from the Past algorithm of Propp and Wilson is a good technique for sampling from and proving the existence of stationary distributions for Markov chains. In this talk, we discuss the proof of the technique. Briefly, the system works by constructing sequences sample paths whose initial states are determined by the previous element in the sequence, so that the original states are ``pushed to minus infinity'', thus establishing the coupling and convergence. This technique has applications to a wide variety of fields; one such application to interference queueing will be discussed in the next talk.

Thursday, September 30, 2021

2:00 pm in Altgeld Hall 347,Thursday, September 30, 2021

Coupling from the Past 2

Aditya S. Gopalan (UIUC ISE)

Abstract: We give a coupling from the past proof for the existence of a stationary distribution for interference queueing networks on grids. This talk highlights the use of this technique for purposes other than sampling, for which it was developed.

Thursday, October 7, 2021

2:00 pm in Altgeld Hall 347,Thursday, October 7, 2021

Use of couplings in distributional convergence

Grigory Terlov (UIUC MATH)

Abstract: It was mentioned in previous talks that bounding distance between two distributions in appropriate metric is often equivalent to finding a good coupling of random variables. In this talk we will build up on that idea and study the use of couplings in bounding total variation distance between two counting random variables. We will apply these techniques to head runs in a sequence of independent coin tosses and occupancy problem as well as other models if time permits. This talk serves as introduction to the Chen-Stein method for Poisson approximation, on which we will focus in the second talk.

Thursday, October 14, 2021

2:00 pm in Altgeld Hall 347,Thursday, October 14, 2021

Use of couplings in distributional convergence (Part2: Stein-Chen method)

Grigory Terlov (UIUC Math )

Abstract: At the end of the last lecture I presented two results due to C. Stein and L.H.Y. Chen that utilize couplings to prove convergence to Poisson distribution. These techniques allow for dependence among random variables and give explicit rate of convergence. In this talk I will explain the main idea behind Stein-Chen method and prove both of the theorems stated last time.