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001484393 001__ 1484393
001484393 003__ OCoLC
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001484393 019__ $$a1410493995$$a1410593638
001484393 020__ $$a9783031368547$$q(electronic bk.)
001484393 020__ $$a3031368541$$q(electronic bk.)
001484393 020__ $$z9783031368530
001484393 020__ $$z3031368533
001484393 0247_ $$a10.1007/978-3-031-36854-7$$2doi
001484393 035__ $$aSP(OCoLC)1410957065
001484393 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dYDX$$dOCLCO
001484393 049__ $$aISEA
001484393 050_4 $$aQA273$$b.C87 2023
001484393 08204 $$a519.2$$223/eng/20231129
001484393 1001_ $$aCurien, Nicolas,$$eauthor.
001484393 24510 $$aPeeling random planar maps :$$bÉcole d'Été de Probabilités de Saint-Flour XLIX -- 2019 /$$cNicolas Curien.
001484393 264_1 $$aCham :$$bSpringer,$$c2023.
001484393 300__ $$a1 online resource (xviii, 286 pages) :$$billustrations (some color).
001484393 336__ $$atext$$btxt$$2rdacontent
001484393 337__ $$acomputer$$bc$$2rdamedia
001484393 338__ $$aonline resource$$bcr$$2rdacarrier
001484393 4901_ $$aÉcole d'Été de Probabilités de Saint-Flour ;$$v2335
001484393 504__ $$aIncludes bibliographical references.
001484393 5050_ $$aIntro -- Introduction -- These Lecture Notes (Do Not) Contain -- Contents -- Part I (Planar) Maps -- 1 Discrete Random Surfaces in High Genus -- 1.1 What Is a Map? Different Points of View -- 1.1.1 Gluing of Polygons and a First Exploration -- Genus -- 1.1.2 Other Definitions of Maps -- Via Permutations -- Embedded Graphs -- 1.1.3 Duality -- 1.2 Geometry and Topology of Uniform Maps -- 1.2.1 Enumeration ``à la Tutte'' -- 1.2.2 Uniform Maps Are Almost Uniform Permutations -- Geometric and Topological Properties of a Uniform Map
001484393 5058_ $$a1.3 Exploring Random Maps with Prescribed Faces and a Conjecture -- 1.3.1 Random Gluing of Prescribed Polygons -- 1.3.2 Peeling Explorations of MP -- 1.3.3 Examples of Peeling Explorations -- Conclusion: Impose Topological Constraints! -- 2 Why Are Planar Maps Exceptional? -- 2.1 Finite and Infinite Planar Maps -- 2.1.1 Finite Planar Maps -- 2.1.2 Local Topology and Infinite Maps -- 2.1.3 Infinite Maps of the Plane and the Half-Plane -- 2.2 Euler's Formula and Applications -- 2.2.1 k-Angulations and Bipartite Maps -- 2.2.2 Platonic Solids -- 2.2.3 Fàry Theorem -- 2.2.4 6-5-4 Color Theorem
001484393 5058_ $$a2.2.5 Moser's circle -- 2.3 Faithful Representations of Planar Maps -- 2.3.1 Tutte's Barycentric Embedding -- 2.3.2 Circle Packing -- 3 The Miraculous Enumeration of Bipartite Maps -- 3.1 Maps with a Boundary and a Target -- 3.1.1 Maps with a Boundary -- 3.1.2 Maps with a Target -- 3.2 Counting Planar Maps and Tutte's Equation -- 3.2.1 The Case of Quadrangulations -- 3.2.2 Boltzmann Maps and Tutte Slicing Formula -- 3.3 Formulas for Disk Partition Functions -- 3.3.1 Boltzmann Measure -- 3.3.2 Admissibility -- 3.4 Getting Our Hands on W() -- 3.4.1 Towards an Expression for W()
001484393 5058_ $$a3.4.2 Back to the Admissibility Criterion -- 3.5 Examples -- 3.5.1 2p-Angulations -- 3.5.2 Uniform Bipartite Maps -- 3.5.3 Triangulations -- 3.5.4 Canonical Stable Maps -- Part II Peeling Explorations -- 4 Peeling of Finite Boltzmann Maps -- 4.1 Peeling Processes -- 4.1.1 Gluing Maps with a Boundary -- 4.1.2 Peeling Process -- 4.1.3 Peeling Process with a Target and Filled-in Explorations -- 4.2 Law of the Peeling Under the Boltzmann Measures -- 4.2.1 q-Boltzmann Maps -- 4.2.2 q-Boltzmann Maps Without Target -- 4.2.3 q-Boltzmann Maps with Target
001484393 506__ $$aAccess limited to authorized users.
001484393 520__ $$aThese Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...). A "Markovian" approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface. Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhD students and researchers interested in graph theory, combinatorial probability and geometry. Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps.
001484393 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 29, 2023).
001484393 650_6 $$aProbabilités.
001484393 650_6 $$aGéométrie.
001484393 650_0 $$aProbabilities.
001484393 650_0 $$aGraph theory.
001484393 650_0 $$aGeometry.$$0(DLC)sh2002004432
001484393 655_0 $$aElectronic books.
001484393 77608 $$iPrint version:$$aCurien, Nicolas$$tPeeling Random Planar Maps$$dCham : Springer,c2023
001484393 830_0 $$aLecture notes in mathematics (Springer-Verlag).$$pÉcole d'été de probabilités de Saint-Flour.
001484393 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2335.
001484393 852__ $$bebk
001484393 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-36854-7$$zOnline Access$$91397441.1
001484393 909CO $$ooai:library.usi.edu:1484393$$pGLOBAL_SET
001484393 980__ $$aBIB
001484393 980__ $$aEBOOK
001484393 982__ $$aEbook
001484393 983__ $$aOnline
001484393 994__ $$a92$$bISE