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Events During the Week of August 7th through August 14th, 2022

Monday, August 8th, 2022

Random Entanglement and History-Dependent Random Sequences
Time: 1:00 pm
Place: 4272 Chamberlin Hall
Speaker: Gage Bonner, Physics PhD Graduate Student
Abstract: This thesis is comprised of two main parts, each concerned with a different stochastic process. In the first section, we consider a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. In the limit of small windows, we appeal to the narrow escape problem to construct a Markov chain on the fundamental groupoid of the region. Taking the transition probabilities between windows as inputs, our Markov chain can be cast as a random walk on a regular language. We obtain a law of large numbers as well as a central limit theorem for this process in which the constants appearing in the limit theorems are expressed in terms of a coupled system of quadratic equations. Our result requires the solution of a simpler problem than those seen previously in the literature, and requires less assumptions.

In the second section, we consider several history-dependent sequences which have attracted recent interest. We primarily study the Ulam-Kac adder, a sequence for which very little is known explicitly except for its first two moments, which have been computed in some generality. Our main contribution is to compute the asymptotic behavior of all moments and obtain bounds on their size. We also provide a semi-analytic formulation of the moment problem which allows them to be computed directly. We discuss many combinatorial interpretations of this sequence and others which, in particular, lead to a novel formula for the first passage times of a related sequence. Connections of these sequences to other areas of mathematics and physics are explored.
Host: Jean-Luc Thiffeault and Lisa Everett
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Tuesday, August 9th, 2022

Election Day
Time: 7:00 am
Abstract: Primary election includes Governor, Congress, State Legislature. Primary election includes Governor, Congress, State Legislature, Attorney General, Lt. Gov, Sec of State, Treasurer, Clerk of Circuit Court, and Sheriff. Go to MyVote.wi.gov to find your polling place, see what is on your ballot, and check your registration. If you are not registered at your current address, you can register at your polling place on Election Day. See vote.wisc.edu for information on registration and voter ID. (The final election for these contests will be November 8.) CONTACT: malischke@wisc.edu URL:
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Wednesday, August 10th, 2022

No events scheduled

Thursday, August 11th, 2022

On the Measurement of Graphene Systems using Scanned Probe Techniques
Time: 9:00 am
Place: Chamberlin 5280
Speaker: Wyatt Behn , Physics PhD Graduate Student
Host: Victor Brar
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Friday, August 12th, 2022

No events scheduled