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We prove an extension of the shape result of Blach`ere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs..
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,
One can also consult [5] and [10] for applications of norm-entropy inequalities to the study of conditional principles of Gibbs type for empirical measures and random
In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
A class of discrete renewal processes with exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in
assumed to be continuous, the corresponding Markov chain will have the weak Feller property. The fact that a process is topologically recurrent also implies that.. it has some
Keywords: Key words: Lipschitz domains, Neumann problem, reflecting Brownian motion, mixed boundary problem, Skorokhod equation, weak uniqueness, uniqueness in law,
Polynomials (2.1) satisfy the following very useful identity originally formulated for so called contin- uous q − Hermite polynomials h n (can be found in e.g.. First assertions
