Lecturer: Stefan Adams TA for the support class: William Nollett
Schedule: Monday 10-11 am room B3.03; Tuesday 3-4 pm room MS.03; Thursday 5-6 pm room MS.04
Support class starts week 2; Thursday 11-12, B1.01; Revision class Friday 7th May, 10-12 am room B3.02
Assessment: exam (85 %), example sheets (15 %). There are 6 example sheets (sheet 1,2,3,5 for credit), and sheet 6 is a Mock exam which is very close to the exam in term 3.
week 1: Discrete time random walks and basics in probability
week 2: Markov property and transition function; Poisson process; random walks
week 3: Q-Matrix and its exponentials
week 4: Forward and backward equations
week 5: Birth processes; hitting times; recurrence and transience
week 6: Invariant distribution
week 7: Ergodic theorem, convergence to equilibrium
week 8: Introduction to percolation
week 9: Peierl's argument; critical value; FKG inequality; Harris Theorem
week 10: Ruso-Seymour-Welsh Theorem/method (crossing of rectangles); Kesten's Theorem; p_c=1/2 for bond percolation on Z2
D.W. Stroock: An Introduction to Markov Processes, Springer (2005).
J. Norris: Markov chains, Cambridge University Press (1997).
G.F. Lawler, L.N. Coyle: Lectures on Contemporary Probability, American MAthematical Society (2000).