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[null,"1.","Record Nr.",null,"UNINA9910955870103321"]
[null,null,"Autore",null,"Stanley Matthew E."]
[null,null,"Titolo",null,"The Loyal West : Civil War and Reunion in Middle America / / Matthew E. Stanley"]
[null,null,"Pubbl/distr/stampa",null,"Urbana, : University of Illinois Press, 2016"]
[null,null,"ISBN",null,"9780252099175"]
[{"$nulls":4},"0252099176"]
[null,null,"Descrizione fisica",null,"1 online resource : illustrations (black and white), map (black and white)"]
[null,null,"Disciplina",null,"977.02"]
[null,null,"Soggetti",null,"Borderlands - Ohio River Valley - History - 19th century"]
[{"$nulls":4},"Reconstruction (U.S. history, 1865-1877) - Ohio River Valley"]
[{"$nulls":4},"Electronic books."]
[{"$nulls":4},"United States History Civil War, 1861-1865 Social aspects"]
[{"$nulls":4},"Ohio History, Local 19th century"]
[{"$nulls":4},"Indiana History, Local 19th century"]
[{"$nulls":4},"Illinois History, Local 19th century"]
[{"$nulls":4},"Ohio River Valley History Civil War, 1861-1865 Social aspects"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Previously issued in print: 2017."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Introduction: the geography embodied: loyal westerners in war and peace -- The progeny of Jamestown: racial construction and western identity on the Dixie frontier -- The boundary between contending nations: border war and restraints on western unity -- The war fattens on the blood of western men: the limits of practical abolitionism on slavery's western border -- The great brotherhood of the west: the demise of the antebellum west and the construction of the loyal west -- Was it for this you fought?: retreat from Reconstruction, the new white supremacy in the loyal west -- Never checked--always victorious: the heyday of the loyal west -- Solely to suppress the rebellion: commemorating conservative unionism in the loyal west -- Epilogue: no more shall the winding rivers be red: reconciliation and the passing of the loyal west."]
[null,null,null,"Sommario/riassunto","'The Loyal West' examines identity and memory among Union soldiers and veterans in the Lower Middle West, a previously overlooked region."]
[null,"2.","Record Nr.",null,"UNINA9910765476803321"]
[null,null,"Autore",null,"Curien Nicolas"]
[null,null,"Titolo",null,"Peeling Random Planar Maps : École d’Été de Probabilités de Saint-Flour XLIX – 2019 / / by Nicolas Curien"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023"]
[null,null,"ISBN",null,"9783031368547"]
[{"$nulls":4},"3031368541"]
[null,null,"Edizione",null,"[1st ed. 2023.]"]
[null,null,"Descrizione fisica",null,"1 online resource (293 pages)"]
[null,null,"Collana",null,"École d'Été de Probabilités de Saint-Flour ; ; 2335"]
[null,null,"Disciplina",null,"519.2"]
[null,null,"Soggetti",null,"Probabilities"]
[{"$nulls":4},"Graph theory"]
[{"$nulls":4},"Geometry"]
[{"$nulls":4},"Stochastic processes"]
[{"$nulls":4},"Graph Theory in Probability"]
[{"$nulls":4},"Probability Theory"]
[{"$nulls":4},"Stochastic Processes"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Introduction -- These Lecture Notes (Do Not) Contain -- Contents -- Part I (Planar) Maps -- 1 Discrete Random Surfaces in High Genus -- 1.1 What Is a Map? Different Points of View -- 1.1.1 Gluing of Polygons and a First Exploration -- Genus -- 1.1.2 Other Definitions of Maps -- Via Permutations -- Embedded Graphs -- 1.1.3 Duality -- 1.2 Geometry and Topology of Uniform Maps -- 1.2.1 Enumeration ``à la Tutte'' -- 1.2.2 Uniform Maps Are Almost Uniform Permutations -- Geometric and Topological Properties of a Uniform Map -- 1.3 Exploring Random Maps with Prescribed Faces and a Conjecture -- 1.3.1 Random Gluing of Prescribed Polygons -- 1.3.2 Peeling Explorations of MP -- 1.3.3 Examples of Peeling Explorations -- Conclusion: Impose Topological Constraints! -- 2 Why Are Planar Maps Exceptional? -- 2.1 Finite and Infinite Planar Maps -- 2.1.1 Finite Planar Maps -- 2.1.2 Local Topology and Infinite Maps -- 2.1.3 Infinite Maps of the Plane and the Half-Plane -- 2.2 Euler's Formula and Applications -- 2.2.1 k-Angulations and Bipartite Maps -- 2.2.2 Platonic Solids -- 2.2.3 Fàry Theorem -- 2.2.4 6-5-4 Color Theorem -- 2.2.5 Moser's circle -- 2.3 Faithful Representations of Planar Maps -- 2.3.1 Tutte's Barycentric Embedding -- 2.3.2 Circle Packing -- 3 The Miraculous "]
[{"$nulls":4},"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() -- 3.4.2 Back to the Admissibility Criterion -- 3.5 Examples -- 3.5.1 2p-Angulations -- 3.5.2 Uniform Bipartite Maps -- 3.5.3 Triangulations."]
[{"$nulls":4},"3.5.4 Canonical Stable Maps -- Part II Peeling Explorations -- 4 Peeling of Finite Boltzmann Maps -- 4.1 Peeling Processes -- 4.1.1 Gluing Maps with a Boundary -- 4.1.2 Peeling Process -- 4.1.3 Peeling Process with a Target and Filled-in Explorations -- 4.2 Law of the Peeling Under the Boltzmann Measures -- 4.2.1  q-Boltzmann Maps -- 4.2.2  q-Boltzmann Maps Without Target -- 4.2.3  q-Boltzmann Maps with Target -- 4.3 Simple Submaps and Simple Peeling Explorations -- 4.3.1 Maps with Simple Boundary -- 4.3.2 Simple Submaps -- 4.3.3 Simple Peeling Exploration -- 4.3.4 Law of the Simple Peeling Under the Boltzmann Measure -- 5 Classification of Weight Sequences -- 5.1 The ν-Random Walk -- 5.1.1 The Step Distribution ν -- 5.1.2 Probabilistic Interpretation of the h↓p-Transformation -- 5.2 Critical Weight Sequences -- 5.2.1 Equivalent Definitions of Criticality -- 5.2.2 h↑-Transform -- 5.3 Discrete Stable Weight Sequences -- 5.3.1 Subcritical Case: a= 32 -- 5.3.2 Critical Generic Case: a= 52 -- 5.3.3 Critical Non-generic: a (3/2 -- 5/2) -- 5.3.4 Examples -- Part III Infinite Boltzmann Maps -- 6 Infinite Boltzmann Maps of the Half-Plane -- 6.1 The Half-Planar Boltzmann Map -- 6.1.1 Characterizing  P(∞) -- 6.1.2 Peeling Process Under  P(∞) -- 6.1.3 Constructing  P(∞) -- 6.1.4 P(∞) as the Weak Limit of  P() as ∞ -- 6.2 Basic Properties -- 6.2.1 Translation Invariance and Ergodicity -- 6.2.2 Cut-Edges and Cut-Points -- 7 Infinite Boltzmann Maps of the Plane -- 7.1 Infinite Boltzmann Maps of the Plane -- 7.1.1 Characterizing  P()∞ -- 7.1.2 Peeling Process Under  P()∞ -- 7.1.3 Constructing  P()∞ -- 7.1.4 P()∞ as the Limit of Maps Conditioned to be Large -- 7.2 Basic Properties -- 7.2.1 Stationarity and Reversibility -- 7.2.2 Ergodicity -- 8 Hyperbolic Random Maps -- 8.1 Constructions -- 8.2 Basic Properties -- 8.2.1 Stationarity, Reversibility and Ergodicity."]
[{"$nulls":4},"8.2.2 Anchored Expansion -- 9 Simple Boundary, Yet a Bit More Complicated -- 9.1 Enumeration of Maps with a Simple Boundary -- 9.1.1 The Core Decomposition -- 9.1.2 Free Boltzmann Map and Exploration of the Core -- 9.2 Infinite ∂-Simple Boltzmann Maps of the Half-Plane -- 9.2.1 Defining  M̃(∞) and  (∞) -- 9.2.2 Simple Peeling Exploration of (∞) -- 9.2.3  (∞) as the Weak Limit of  () -- 9.3 Basic Properties -- 10 Scaling Limit for the Peeling Process -- 10.1 Invariance Principles for the Perimeter Process -- 10.1.1 The Case of the ν-Walk S -- 10.1.2 The Cases of S↑ and S↓ -- 10.2 Scaling Limit for the Volume Process -- 10.2.1 Stable Limit for the Volume of Boltzmann Maps -- 10.2.2 Functional Scaling Limit for the Volume and Perimeter Processes -- 10.2.3 Law of ``Iterated'' Logarithm -- 10.3 Scaling Limits in the Hyperbolic Regime -- 10.4 Markovian Explorations Are Always Roundish -- Part IV Percolation(s) -- 11 Percolation Thresholds in the Half-Plane -- 11.1 Prerequisites -- 11.1.1 Randomized Peeling Process -- 11.1.2 Mean Gulp and Exposure -- 11.2 Face Percolation -- 11.2.1 Annealed Threshold and Exploration of Face Percolation -- 11.2.2 Proof of Theorem 11.3 -- 11.2.3 Dual Exploration -- 11.2.4 Degree Percolation -- 11.3 Bond Percolation -- 11.3.1 A Heuristic Before the Proof: Adding Faces of Degree 2 -- 11.3.2 The True Proof: Adding Crosses! -- 11.4 Site Percolation and the Simple Peeling -- "]
[{"$nulls":4},"11.4.1 Back to Bond and Face Percolations -- 11.4.2 Site Percolation -- 12 More on Bond Percolation -- 12.1 Critical Exponents in the Half-Plane -- 12.1.1 Length of Exploration -- 12.1.2 More Open Questions -- 12.2 A Boltzmann Approach to Bond Percolation -- 12.2.1 Duality of Stable Maps Via Percolation -- 12.2.2 Critical Exponents and Open Questions -- 12.3 Percolations on M∞ -- 12.3.1 Do Plane and Half-Plane Bond Percolation Thresholds Coincide?."]
[{"$nulls":4},"12.3.2 Open Questions -- 12.4 Percolation on Hyperbolic Random Maps -- 12.4.1 Critical and Uniqueness Thresholds -- 12.4.2 Open Questions -- Part V Geometry -- 13 Metric Growths -- 13.1 Eden Model: Exponential FPP Distances on the Dual -- 13.1.1 Definition of the Eden Distance -- 13.1.2 Uniform Peeling -- 13.1.3 Fpp Growth on  M∞ -- 13.1.4 Fpp Growth on  H∞ -- 13.2 Dual Graph Distances -- 13.2.1 Exploration of Dual Metric -- 13.2.2 Growth of the Dual Metric in  M∞ -- 13.2.3 Growth of the Dual Metric on  H∞ -- 13.2.4 Cut-Points in the Dense Phase -- 13.3 Primal Graph Distances -- 13.3.1 Triangulations -- 13.3.2 Quadrangulations -- 13.3.3 General Case -- 13.4 … and for the Half-Plane ? -- 14 A Taste of Scaling Limit -- 14.1 Gromov-Hausdorff Topology -- 14.1.1 Space of Metric Spaces -- 14.1.2 Gromov-Hausdorff Topology -- 14.1.3 Properties -- 14.2 Scaling Limits for Large Boltzmann Maps -- 14.2.1 The Brownian Sphere -- 14.2.2 The Stable Maps -- 14.3 Scaling Limit for Dual Maps and Growth-Fragmentation Trees -- 14.3.1 Genealogy on Holes -- 14.3.2 Slicing at Heights -- Part VI Simple Random Walk -- 15 Recurrence, Transience, Liouville and Speed -- 15.1 M∞ Is Recurrent -- 15.1.1 Discrete Uniformization of Infinite Planar Graphs -- 15.1.2 Benjamini-Schramm Limits -- 15.2 Simple Random Walk on M∞ -- 15.2.1 Transience of M∞ in the Dense Case -- 15.2.2 Intersection and Recurrence -- 15.3 Hyperbolic Maps and Positive Speed -- 15.3.1 Anchored Expansion, Speed and Stationarity -- 16 Subdiffusivity and Pioneer Points -- 16.1 Pioneer Points and Subdiffusivity -- 16.1.1 Pioneer Points -- 16.1.2 Primal Distances -- 16.1.3 About Tentacles -- 16.2 Subdiffusivity via Stationarity -- 16.2.1 Subdiffusivity from Diffusivity on a Sparse Subgraph -- 16.2.2 Heuristic for G_R -- A Elements of Fluctuation Theory -- A.1 Oscillations, Duality -- A.2 Cyclic Lemma and Applications."]
[{"$nulls":4},"A.2.1 Feller's Cyclic Lemma -- A.2.2 Applications -- Skip-Free Walks -- Plane Trees -- A.3 Random Walks Conditioned to Stay Positive -- A.3.1 h-Transform of Markov Chains -- A.3.2 Renewal Function -- A.3.3 Oscillating Case and Limit of Large Conditionings -- A.3.4 Tanaka's Construction -- A.3.5 Drift to -∞ and Cramér's Condition -- A.4 Ratio and Local Limit Theorem -- A.4.1 Strong Ratio Limit Theorem -- A.4.2 Local Limit Theorem -- B Coding of Bipartite Maps with Labeled Trees -- B.1 Bouttier-Di Francesco-Guitter Coding of Bipartite Maps -- B.1.1 From Maps to Trees -- B.1.2 From Trees to Maps -- B.2 Distribution of the Forest of Mobiles -- B.2.1 Janson and Stefansson's Trick -- B.2.2 Law of the Unlabeled Forest -- B.3 Back to the Enumeration Results -- B.3.1 Back to the Admissibility Criterion -- B.3.2 Interpretation of the Law J and Back to Criticality -- Bibliography."]
[null,null,null,"Sommario/riassunto","These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...). A “Markovian” approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as \"peeling "]
[{"$nulls":4},"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 PhDstudents 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."]