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...

If a Markov chain converges rapidly to stationarity, then the time until the first hit on a rarely-visited set of states is approximately exponentially distributed; moreover an explicit bound for the error in this approximation can be given. This complements results of Keilson.

Consider a Poisson process of unit squares in the plane, with intensity [theta]. Let q(L, [theta]) be the chance that an L x L square is completely covered by the randomly-positioned unit squares. Stein's method is used to give explicit bounds on q(L, [theta]), improving on the known asymptotic...

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.