LEADER 04413nam 22007095 450 001 9910300158103321 005 20220404225526.0 010 $a3-319-05852-5 024 7 $a10.1007/978-3-319-05852-8 035 $a(CKB)3710000000111924 035 $a(EBL)1731084 035 $a(OCoLC)884584871 035 $a(SSID)ssj0001243995 035 $a(PQKBManifestationID)11691598 035 $a(PQKBTitleCode)TC0001243995 035 $a(PQKBWorkID)11312482 035 $a(PQKB)11747538 035 $a(MiAaPQ)EBC1731084 035 $a(DE-He213)978-3-319-05852-8 035 $a(PPN)178781096 035 $a(EXLCZ)993710000000111924 100 $a20140506d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to random interlacements /$fby Alexander Drewitz, Balįzs Rįth, Artėm Sapozhnikov 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (124 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-05851-7 320 $aIncludes bibliographical references and index. 327 $aRandom Walk, Green Function, Equilibrium Measure -- Random Interlacements: First Definition and Basic Properties.- Random Walk on the Torus and Random Interlacements.- Poisson Point Processes.- Random Interlacements Point Process.- Percolation of the Vacant Set.- Source of Correlations and Decorrelation via Coupling.- Decoupling Inequalities -- Phase Transition of Vu -- Coupling of Point Measures of Excursions. 330 $aThis book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aProbabilities 606 $aOperations research 606 $aManagement science 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aOperations Research, Management Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M26024 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aProbabilities. 615 0$aOperations research. 615 0$aManagement science. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aOperations Research, Management Science. 615 24$aApplications of Mathematics. 676 $a519.2 700 $aDrewitz$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721620 702 $aRįth$b Balįzs$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSapozhnikov$b Artėm$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300158103321 996 $aAn Introduction to Random Interlacements$92536505 997 $aUNINA