Hello,
I am a final year undergraduate student in pure mathematics at The Hong Kong University of Science and Technology. Previously, I was a visitor at Monash University and an exchange student at The University of British Columbia, Vancouver.
I spend most of my time in and around probability theory, especially on topics with a geometric or physical flavour. Most recently, I have been working on percolation.
Email: zhang_baining@outlook.somethingabsolutelydiabolical.com
Notes
Some links to resources
Random Walks in Random Environments
Session 2 - The Environment Viewed from the Particle
Directed Polymers
Not much here until I get out a preprint. 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 for an undergraduate research project on self-avoiding walks on random conductances and supercritical percolation clusters. We extend the setting of a paper by Chino and Sakai to i.i.d. conductances on infinite graphs with bounded degree.
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.
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.
Update 2026-10-05:
Errata by AI
An errata generated with GPT-6 Astra is provided here for convenience. I have not read all of it and claim no authorship.
Loop-Erased Random Walks
I learned this as a part of SCIE 2500 Guided Study on Research II. 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 is not the easiest to read. 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
These notes are messy and are available here mainly for convenience.
MATH 5380 (Topics in) Combinatorics
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.
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 handwritten notes taken from lecture videos of a course by Chenlin Gu. Contains many mistakes which I do not intend to fix.
The lectures are in Chinese. My notes are in English.
Course Webpage (with lecture videos)
Note 1
Note 2
Note 3
Note 4
Note 5