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We analyze a class of spatial random spanning trees built on a realization ofa homogeneous Poisson point process of the plane. This tree has a simple radialstructure with the origin as its root. We first use stochastic geometryarguments to analyze local functionals of the random tree such as thedistribution of the length of the edges or the mean degree of the vertices. Faraway from the origin, these local properties are shown to be close to those ofa variant of the directed spanning tree introduced by Bhatt and Roy. We thenuse the theory of continuous state space Markov chains to analyze some nonlocalproperties of the tree, such as the shape and structure of its semi-infinitepaths or the shape of the set of its vertices less than $k$ generations awayfrom the origin. This class of spanning trees has applications in many fieldsand, in particular, in communications.

The radial spanning tree of a Poisson point process