Article ID Journal Published Year Pages File Type
6873803 Information and Computation 2018 18 Pages PDF
Abstract
In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by independence assumptions. In this work we initiate an effort to bridge this gap by developing tools that allow us to work with independence without assuming it. Let Gn be the set of all graphs on n vertices and let S be an arbitrary subset of Gn, e.g., the set of all graphs with m edges. The study of random networks can be seen as the study of properties that are true for most elements of S, i.e., that are true with high probability for a uniformly random element of S. With this in mind, we pursue the following question: What are general sufficient conditions for the uniform measure on a set of graphsS⊆Gnto be well-approximable by a product measure on the set of all possible edges?
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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