Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6873803 | Information and Computation | 2018 | 18 Pages |
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 graphsSâGnto 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
Authors
Dimitris Achlioptas, Paris Siminelakis,