Baining Zhang’s Homepage
Hello, I am a third year undergraduate student at HKUST, currently on exchange at UBC Vancouver.
Academic Interests
I am mainly interested in probability theory and related fields, including mathematical physics and various kinds of geometry. Most recently, I have been studying random walks (in random environments).
Notes
Towards Schramm-Loewner Evolutions
This set of notes was completed during a reading course titled Conformally Invariant Processes in the Plane. The part on capacity and half-plane capacity is poorly written.
A list of references which I found helpful is included at the end of the notes.
Loop-Erased Random Walks
This topic was learned as a part of my SCIE 2500 Guided Study on Research II project. The reports and presentation can be found below. Note however that due to length limitations, they only provide glimpses of an introduction to LERWs.
Progress Report
Final Report
Presentation Slides
Lawler has a book Random Explorations on this topic. He also has a set of notes titled Topics in loop measures and the loop-erased walk, which has many typos. I recommend reading Random Explorations first.
Self-Avoiding Walks in Random Environments
The following report was written in the context of an undergraduate ‘research’ project on self-avoiding walks in random conductances and supercritical percolation clusters. We slightly modify the setting of the problem in a paper by Chino and Sakai and essentially show that the same proof still works in the new setting.
The Quenched Critical Point of Self-Avoiding Walk on Infinite Graphs with Random Conductances
Random Walks and Homogenization Theory
Incomplete poorly handwritten notes taken from lecture videos of a course by Chenlin Gu. Certainly contain a lot of mistakes. Why do I even put them up here?
Course Webpage
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
I will return to this after a course on PDEs. (Which is never because analysis is dead at HKUST.)
The Brownian Map
Coming soon (in a few months).