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In discrete time, studies of quantitative convergence rates have been motivated largely by Markov chain Monte Carlo algorithms (see Gelfand and Smith, 1990; Smith and Roberts,
A class of discrete renewal processes with exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in
Central limit theorems for Markov chains are considered, and in particular the relationships between various expressions for asymptotic variance known from the literature.. These
Keywords: Adaptive Markov chains, Coupling, Markov Chain Monte Carlo, Metropolis Algo- rithm, Stochastic Approximation, Rate of
A question of increasing importance in the Markov chain Monte Carlo literature (Gelfand and Smith, 1990; Smith and Roberts, 1993) is the issue of geometric ergodicity of Markov
In this section we use the large deviation results for the discrete time Markov chain con- sidered in Sections 3, 4 and 5 to obtain the empirical measure LDP for two very
Amongst other things, Aldous proved that the CRT is the scaling limit of a wide class of discrete random trees (in particular it is the scaling limit of uniformly distributed
Molloy, Very rapidly mixing Markov chains for 2∆-colourings and for independent sets in a 4-regular graph, Random Struc. Tetali, Mathematical aspects of mixing times in Markov
