LEADER 02750nam a2200433 i 4500 001 991003626969707536 006 m o d 007 cr cnu|||unuuu 008 190321s2017 sz a ob 101 0 eng d 020 $a9783319658162$q(electronic bk.) 020 $a3319658166$q(electronic bk.) 024 7 $a10.1007/978-3-319-65816-2$2doi 035 $ab1436234x-39ule_inst 082 04$a519.2$223 084 $aAMS 60F10 084 $aAMS 05C80 084 $aLC QA274-274.9 100 1 $aChatterjee, Sourav$0721642 245 10$aLarge deviations for random graphs$h[e-book] :$bÉcole d'Été de Probabilités de Saint-Flour XLV - 2015 /$cby Sourav Chatterjee 260 $aCham :$bSpringer,$c2017 300 $a1 online resource (xi, 170 p.) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 347 $atext file$bPDF$2rda 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2197 505 0 $a1. 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. 520 $aThis book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics 650 0$aProbabilities 650 0$aCombinatorial analysis 650 0$aRandom graphs$vCongresses 650 0$aLarge deviations$vCongresses 776 08$iPrinted edition:$z9783319658155 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-65816-2$zAn electronic book accessible through the World Wide Web 907 $a.b1436234x$b03-03-22$c21-03-19 912 $a991003626969707536 996 $aLarge deviations for random graphs$91749793 997 $aUNISALENTO 998 $ale013$b21-03-19$cm$d@ $e-$feng$gsz $h0$i0