Consider an array of random variables (Xi,j), 1 = i,j [infinity], such that permutations of rows or of columns do not alter the distribution of the array. We show that such an array may be represented as functions f([alpha], [xi]i, [eta]j, [lambda]i,j) of underlying i.i.d, random variables....

Shift-coupling means pasting together the paths of two processes modulo a random shift. This concept can be related to the invariant [sigma]-field in a similar way as ordinary coupling is related to the tail [sigma]-field. We give an expository account of this relationship, implicit in work of...

Start two independent copies of a reversible Markov chain from arbitrary initial states. Then the expected time until they meet is bounded by a constant times the maximum first hitting time for the single chain. This and a sharper result are proved, and several related conjectures are discussed.

A previous paper discussed explicit bounds in the exponential approximation for the distribution of the waiting time until a stationary reversible Markov chain first enters a 'rare' subset of states. In this paper Stein's method is used to get explicit (but complicated) bounds on the Poisson...