Titlebook: Large Deviations for Random Graphs; École d‘Été de Proba Sourav Chatterjee Book 2017 Springer International Publishing AG 2017 Random graph

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Basics of Graph Limit Theory,This chapter summarizes some basic results from graph limit theory. The only background assumed here is the list of results from the previous chapter.

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Applications of Dense Graph Large Deviations,This chapter contains some simple applications of the large deviation principle for dense Erdős–Rényi random graphs that was derived in the previous chapter. The abstract theory yields surprising phase transition phenomena when applied to concrete problems.

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Exponential Random Graph Models,ere . = (.., ., ..) is a vector of real parameters, .., .., ., .. are real-valued functions on ., and .(.) is the normalizing constant. Usually, .. are taken to be counts of various subgraphs, for example ..(.) = number of edges in ., ..(.) = number of triangles in ., etc. These are known as exponen

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Large Deviations for Sparse Graphs,ior 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 theore

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Book 2017ics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics..

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