Baining Zhang’s Homepage
Hello, I am a second year undergraduate student at HKUST. I run a more mathematical blog called Peasant Maths.
Academic Interests
I am mainly interested in probability theory and mathematical physics. Recently, I have been studying random walks (in random environments) and percolation.
An idea which I would like to explore is the dream of universality, which (vaguely) says that the behaviour of a large number of random variables is independent of the individual distributions. A first example of universality is the central limit theorem: the rescaled distribution of the mean of a large number of random variables behaves Gaussian. This is still very much the distant goal when proving universality results. To a physicist, universality has been extensively studied using the language of renormalisation groups. Yet, for mathematicians, a rigorous understanding of universal phenomena is still very much a dream. This excellent talk by Martin Hairer should explain more.
Notes
Towards Schramm-Loewner Evolutions
I might write more a complete set of notes.
Loop-Erased Random Walks
This topic was learned as a part of my SCIE 2500 Guided Study on Research II project. The reports which I have written can be found below.
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.
Random Walks and Homogenization Theory
Handwritten notes taken from lecture videos (in Chinese) of a course by Chenlin Gu.
Course Webpage
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5, in preparation
Certainly contain a lot of mistakes. Perhaps I will make better notes on this topic in the future.