In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces whichâ€¦ (More)

Staircase walks are lattice paths from to which take diagonal steps and which never fall below the -axis. A path hitting the -axis times is assigned a weight of where . A simple local Markov chainâ€¦ (More)

We present the first optimal randomized online algorithms for the TCP acknowledgment problem [5] and the Bahncard problem [7]. These problems are well-known to be generalizations of the classicalâ€¦ (More)

Simulated tempering and swapping are two families of sampling algorithms in which a parameter representing temperature varies during the simulation. The hope is that this will overcome bottlenecksâ€¦ (More)

Consider the following Markov chain, whose states are all domino tilings of a 2n 2n chessboard: starting from some arbitrary tiling, pick a 2 2 window uniformly at random. If the four squaresâ€¦ (More)

Monte Carlo algorithms often depend on Markov chains to sample from very large data sets. A key ingredient in the design of an efficient Markov chain is determining rigorous bounds on how quickly theâ€¦ (More)

As a part of the Atmospheric Model Intercomparison Project (AMIP), the behaviour of 15 general circulation models has been analysed in order to diagnose and compare the ability of the differentâ€¦ (More)

We study the behavior of random walks along the edges of the stable marriage lattice for various restricted families of allowable preference sets. In the "k-attribute model," each man is valued inâ€¦ (More)