演講訊息 TALKS

In several talks, I plan to give an introduction to the random walks in a random environment. To mention a simple model, we consider the simple random walk on 1-d lattice moves one step to the right with probability p and to the left with probability (1-p). In a random environment (denoted by (pi(ω)) , the random walk with current location at i moves one step to the right on the lattice with probability pi (ω) and to the left with probability (1-pi(ω)). This is a simple example of a random walk in a random environment. The behaviors of a simple random walk are well known and rich . Its average speed (in large time) is 2p-1. The fluctuation (along the average speed) is normal. The large deviation principle holds. There are many more rich results (see Revesz). The behaviors of the random walk in a random environment will depend on the random property of the environment. Similar to the simple random walk, the goal is to understand its average speed, its fluctuation, and its large deviation properties. This seminar provides a chance to learn interesting results of the subject. We will start with the discussion on the Solomon’s paper, which proves the first result and stimulates further studies.