Graduate Program Events |
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
Tuesday, August 9th, 2022
- Election Day
- Time: 7:00 am - 8:00 pm
- 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:
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
Friday, August 12th, 2022
- No events scheduled