Coupling is a method by which random variables or random processes are put onto a single probability space in such a way that they can be properly compared. Coupling is a powerful technique in probability theory and has been applied in a wide variety of different contexts, e.g. to prove stochastic inequalities, scaling properties, limit theorems, rates of convergence, and asymptotic approximations.
The course first explains what coupling is and what general
framework it fits into. After that, a number of applications
are described, taken from the theory of Markov chains, card shuffling, percolation, random walk, Poisson approximation, perfect simulation, and interacting particle systems.
Voorkennis
Inleiding kansrekening
Tentaminering
Schriftelijk tentamen
Literatuur
T. Lindvall, Lectures on the Coupling Method, John Wiley & Sons, New York, 1992, ISBN 0-471-54025-0. (Sold out but Dover Publication available.)