02750nam a2200433 i 4500991003626969707536m o d cr cnu|||unuuu190321s2017 sz a ob 101 0 eng d9783319658162(electronic bk.)3319658166(electronic bk.)10.1007/978-3-319-65816-2doib1436234x-39ule_inst519.223AMS 60F10AMS 05C80LC QA274-274.9Chatterjee, Sourav721642Large deviations for random graphs[e-book] :École d'Été de Probabilités de Saint-Flour XLV - 2015 /by Sourav ChatterjeeCham :Springer,20171 online resource (xi, 170 p.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture notes in mathematics,0075-8434 ;21971. Introduction -- 2. Preparation -- 3. Basics of graph limit theory -- 4. Large deviation preliminaries -- 5. Large deviations for dense random graphs -- 6. Applications of dense graph large deviations -- 7. Exponential random graph models -- 8. Large deviations for sparse graphs -- Index.This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, 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 statisticsProbabilitiesCombinatorial analysisRandom graphsCongressesLarge deviationsCongressesPrinted edition:9783319658155https://link.springer.com/book/10.1007/978-3-319-65816-2An electronic book accessible through the World Wide Web.b1436234x03-03-2221-03-19991003626969707536Large deviations for random graphs1749793UNISALENTOle01321-03-19m@ -engsz 00