Abstract
This paper is a contribution to the study of the relationship between causal sets and Lorentzian manifolds. Given a causal set and a local region in it, identified with the interval between two elements, we use the distributions of chain and maximal-chain lengths in that region as a tool for establishing to what extent the region is manifoldlike. We first derive the mean length distributions for causal sets obtained from uniformly random sets of points in Minkowski space, in a form suitable to addressing our question. We then compare those distributions with the ones obtained from some examples of non-manifoldlike causal sets and, for manifoldlike causal sets, we compare some dimension estimators derived from the length distributions with other available dimension estimators.
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