## Week 11 - lecture 1

## Week 10 - lecture 2

## Week 10 - lecture 1

## Week 9 - lecture 2

## Week 9 - lecture 1

## Week 8 - lecture 2

1.* Let be an irreducible transition matrix on , and suppose that is nonzero and satisfies . (a) Show that for all odd . (b) Deduce that there is a partition of into two sets such that if , then either and , or and . 2.* Let be an irreducible transition matrix on , […]

## Week 8 - lecture 1

## Week 7 - lecture 2

## Week 7 - lecture 1

## Week 6 - lecture 2

1.* (Review problem). Suppose that we move a knight randomly on a standard chess board according to the following rules. Initially, the knight stands on one of the corners of the chess board. Then, at each step, the knight chooses one of the possible moves at random with equal probabilities, independently of what happened before. […]