Student Probability Seminar

Purdue University, spring 2020

Thursdays at 3:30 in REC 316.

The goal of this seminar is for students (and the occasional professor) to give introductions to various areas of probability or important concepts in probability. The talks should be accessible to anyone who has any graduate-level background in probability. Talks are done with chalk and last 50 minutes. Questions are encouraged during and after the talks. Please send comments and suggestions to the seminar organizer, Daniel Slonim.

For a list of talks from past semesters, click here.

Date

Speaker

Title
1/30/2020 Zack Selk Beyond Ito's integral - Skorokhod Integration through Wiener Chaos Expansion
Abstract
In this talk I will talk about the limitations of Ito integration, I will introduce Wiener chaos expansion and use it to define the Skorokhod integral. Skorokhod integration extends stochastic integration to non adapted integrands. It also provides several computational tools including integration by parts.
2/20/2020 Daniel Slonim Loop-Erased Random Walks and Spanning Trees on Markov Chains
Abstract
The loop-erased random walk (LERW) was first proposed by Greg Lawler in 1980. Robin Pemantle (1991) showed that the path between two vertices on a uniform spanning tree is distributed like a loop-erased random walk from one to the other, and David Wilson (1996) used this to generate a random spanning tree by means of LERWs. It is natural to first consider the loop-erasure of a nearest-neighbor random walk on a graph where the walk chooses uniformly from the available edges at each step. In this case, Wilson's algorithm generates a uniformly chosen spanning tree. However, the result can be extended to general finite-state Markov chains. The results I present are for finite-state Markov chains with sinks. The proofs are my own, though the results are already known.
Subsequent talks were canceled due to the coronavirus