Random Event Structures

13 years 4 months ago

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Abstract In a line of recent development, probabilistic constructions of universal, homogeneous objects have been provided in various categories of ordered structures, such as causal sets[12] , bifinite domains[13] , and countable partial orders[10] . These constructions have been shown to produce objects with the desired properties with probability 1 in an appropriately defined measure space. A common strategy for these constructions is successive point-wise extension of an existing finite structure, with decisions on the relationships between the newly added point and the existing structure made according to well-specified probabilistic choices. This strategy is a departure from (and understandably so due to the increased complexity) the original one for random graphs[16] where a universal homogeneous countable graph is constructed with probability 1 in a single step (i.e., a single round of countably many probabilistic choices made independently). It would be interesting to see whic...

Manfred Droste, Guo-Qiang Zhang

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