Martin boundary covers Floyd 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...

Martin boundary for some symmetric Lévy processes

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric Lévy processes in R. We show that, if D ⊂ R is an open set which is κ-fat at a boundary point Q ∈ ∂D, then there is exactly one Martin boundary point associated with Q and this Martin boundary point is minimal. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40;...

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.

The Martin Boundary for Random Walk