Reinforced random walk
Student No.:20
Time:Mon & Wed 10:40-12:15,
Instructor:曾小林 Zeng Xiaolin  
Place:Conference Room 2, Jin Chun Yuan West Bldg.
Starting Date:2018-7-2
Ending Date:2018-7-30

Imagine one were to play numerous times slot machines, and one can choose between two machines with different (unknown) winning probabilities, how to choose wisely based on history? A not so curious person wandering in Manhattan city, each time he came across a crossroad, he randomly chooses one direction, with probability proportional to how good he knew the avenue in that direction, will he eventually visit every corner of the city? After this course on random process with memory (reinforcement), we will be able to answer these questions.
We will focus on one particular model: the linear edge reinforced random walk. This is a random walk which interact with its own trajectory, at every step, the process prefers traverse edges already visited, with a bias proportional to the number of visit to the edges. We will give a gentle introduction to the subject. Then we will discuss some recent breakthroughs, if time allows, we will also discuss its surprising relation with a classic phenomenon in quantum diffusion: the Anderson localization.

1. Markov chain and Markov jump process
2. Martingale