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020 _a9783319658162
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024 7 _a10.1007/978-3-319-65816-2
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
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082 0 4 _a519.2
_223
100 1 _aChatterjee, Sourav.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLarge Deviations for Random Graphs
_h[electronic resource] :
_bÉcole d'Été de Probabilités de Saint-Flour XLV - 2015 /
_cby Sourav Chatterjee.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXI, 170 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_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 _aCombinatorics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M27004
650 2 4 _aCombinatorics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M29010
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319658155
776 0 8 _iPrinted edition:
_z9783319658179
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2197
856 4 0 _uhttps://doi.org/10.1007/978-3-319-65816-2
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