LEADER 03040nam 22005175 450 001 9910257379303321 005 20200706111450.0 010 $a3-319-65816-6 024 7 $a10.1007/978-3-319-65816-2 035 $a(CKB)4100000000587421 035 $a(DE-He213)978-3-319-65816-2 035 $a(MiAaPQ)EBC5579572 035 $a(PPN)204533309 035 $a(EXLCZ)994100000000587421 100 $a20170901d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLarge Deviations for Random Graphs $eÉcole d'Été de Probabilités de Saint-Flour XLV - 2015 /$fby Sourav Chatterjee 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XI, 170 p.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2197 311 $a3-319-65815-8 327 $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. 330 $aThis book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2197 606 $aProbabilities 606 $aCombinatorics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aProbabilities. 615 0$aCombinatorics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aCombinatorics. 676 $a511.5 700 $aChatterjee$b Sourav$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721642 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910257379303321 996 $aLarge deviations for random graphs$91749793 997 $aUNINA