Ratio limits and Martin boundary

Phase transition and Martin boundary

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The Max - Plus Martin Boundary

We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of deterministic optimal control problems with additive reward. The analogue of the Martin compactification is seen to be a generalisation of the compactification of metric spaces using (generalised) Busemann functions. We define...

The Martin Boundary for Random Walk

On the Martin Boundary for Markov Chains.

wide compared with the length of the specimen, and so is the angle between the lateral edge of the kink band and the axis of extension, E = [sin xo/sin (xi + so) ] 1. (2) For narrow kink bands and deformation bands, (a) an approximate relation is s = cot (900 w); (b) a more precise relation where a and ,3 are the respective angles between the kink-band boundary and the active glide plane in the...

The Martin Boundary in Non-lipschitz Domains

The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in Cγ domains, where γ(x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.