The Martin Boundary for Random Walk

The Martin Boundary for Random Walk

The Random Walk on the Boundary Method for Calculating Capacitance

Here we consider the problem of the computing the capacitance of a conducting body. The capacitance can be represented as an integral functional of the stationary distribution of particular “random walk on the boundary” Markov chain. The computational algorithm derived from this is used to compute the capacitance of the unit cube with relative error 4× 10−7, the most accurate estimate known.

t-Martin boundary of killed random walks in the quadrant

We compute the t-Martin boundary of two-dimensional small steps random walks killed at the boundary of the quarter plane. We further provide explicit expressions for the (generating functions of the) discrete t-harmonic functions. Our approach is uniform in t, and shows that there are three regimes for the Martin boundary.

Depth Map Boundary Enhancement Using Random Walk

Depth information is essential for depth image-based rendering (DIBR), which is one of the rendering processes for the virtual view using a color image and its corresponding depth map. Although there are several depth estimation methods, more accurate depth estimation is still required. Since inaccurate depth information along object boundaries causes serious rendering errors, depth boundary in...

Martin boundary theory of some quantum random walks

In this paper we define a general setting for Martin boundary theory associated to quantum random walks, and prove a representation theorem. We show that in the dual of a simply connected Lie subgroup of U(n), the extremal Martin boundary is homeomorphic to a sphere. Then, we investigate restriction of quantum random walks to Abelian subalgebras of group algebras, and establish a Ney–Spitzer th...