Hello,
In September, I will be a final year undergraduate student in mathematics at The Hong Kong University of Science and Technology. Currently, I am a Visitor at the School of Mathematics, Monash University.
I am broadly interested in probability theory, with strong tendency towards topics with a geometric or physical flavour. Most recently, I have been studying random walks and percolation.
Email: zhang_baining@outlook.somethingabsolutelydiabolical.com \
Notes
Some resources
Directed Polymers
Not much here until I get out a preprint. This stopping time is likely to be infinite. In the mean time, please check out the following:
Presentation Slides
Excel Simulation for Random Environment, see presentation slides for explanation.
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. In the following report, 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
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, but the proofs should be correct and might be enlightening to some.
An extensive list of references and learning material which I found helpful is included at the end of the notes. In fact this is probably the most helpful part 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. For further content (especially on the uniform spanning forest), I recommend Probability on Trees and Networks by Lyons and Peres.
Archived notes
MATH 5380 (Topics in) Combinatorics
Note which I have taken from the lectures. Like the lectures, these notes view mathematics through an expressionist lens: they are not designed to make complete sense, but are meant to evoke thought. Cheeky remarks aside, there exists a much better version of these notes, which are unfortunately not publicly available.
Lecture 1 - 2026-02-04 (See this preprint for more on Schanuel integration)
Lecture 2 - 2026-02-11
Lecture 3 - 2026-02-25
Lecture 6 - 2026-03-18
Lecture 8 - 2026-04-01
Lecture 9 - 2026-04-15
Lecture 10 - 2026-04-22
Lecture 11 - 2026-04-29
Random Walks and Homogenization Theory
Incomplete poorly handwritten notes taken from lecture videos of a course by Chenlin Gu. Contains many mistakes which I do not intend to fix. These are available here mainly for my ease of access.
The lectures are in Chinese, but my notes are in English.
Course Webpage (with lecture videos)
Note 1
Note 2
Note 3
Note 4
Note 5