Abstract
The results of the previous chapters were derived using tools from graph limit theory. This theory, however, is inadequate for understanding the behavior of sparse graphs. The goal of this chapter is to describe an alternative approach, called nonlinear large deviations, that allows us to prove similar results for sparse graphs. Nonlinear large deviation theory gives a way of getting quantitative error bounds in some of the large deviation theorems proved in earlier chapters. The quantitative error bounds make it possible to extend the results to the sparse regime. At the time of writing this monograph, this theory is not as well-developed as the theory for dense graphs, but developed enough to make some progress about sparse graphs.
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Chatterjee, S. (2017). Large Deviations for Sparse Graphs. In: Large Deviations for Random Graphs. Lecture Notes in Mathematics(), vol 2197. Springer, Cham. https://doi.org/10.1007/978-3-319-65816-2_8
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DOI: https://doi.org/10.1007/978-3-319-65816-2_8
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