Geometric and spectral properties of causal maps
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Abstract
We study the random planar map obtained from a critical, finite variance,
Galton-Watson plane tree by adding the horizontal connections between
successive vertices at each level. This random graph is closely related to the
well-known causal dynamical triangulation that was introduced by Ambj{\o}rn and
Loll and has been studied extensively by physicists. We prove that the
horizontal distances in the graph are smaller than the vertical distances, but
only by a subpolynomial factor: The diameter of the set of vertices at level
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1435-9863