Peeling Random Planar Maps PDF Download
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Author: Nicolas Curien
Publisher: Springer Nature
ISBN: 3031368541
Category : Mathematics
Languages : en
Pages : 293
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Book Description
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 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.
Author: Nicolas Curien
Publisher: Springer Nature
ISBN: 3031368541
Category : Mathematics
Languages : en
Pages : 293
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Book Description
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 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.
Author: Simon Kuestenmacher
Publisher: Hachette UK
ISBN: 1914317149
Category : Reference
Languages : en
Pages : 192
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Book Description
What would the world be without maps? How would we orientate ourselves? How would we travel? How could we plan streets or entire cities? We encounter maps everywhere in everyday life. But they can do much more than just represent the topography of places. The geographer Simon Kuestenmacher collects exciting, entertaining and useful maps that open up a new perspective on the world in an extraordinary way. Where on Earth do most people live? What does the world look like from a dolphin's point of view? What did the world look like in the 17th century? Where in Europe were the last executions carried out? And how much tip is expected in the different countries? All maps represent our living environment in an unusual way, explain connections from new perspectives and show how much fun data and facts are when they are presented in a visually interesting way.
Author: A. A. Dorogovt͡sev
Publisher: VSP
ISBN: 9789067641630
Category : Architecture
Languages : en
Pages : 122
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Book Description
This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.
Author: Jeff Ashworth
Publisher: Media Lab Books
ISBN: 9781948174374
Category : Games & Activities
Languages : en
Pages : 256
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Book Description
For many tabletop RPG players, the joy of an in-depth game is that anything can happen. Typical adventure modules include a map of the adventure’s primary location, but every other location?whether it's a woodland clearing, a random apothecary or the depths of a temple players elect to explore?has to be improvised on the fly by the Game Master. As every GM knows, no matter how many story hooks, maps or NPCs you painstakingly create during session prep, your best-laid plans are often foiled by your players' whims, extreme skill check successes (or critical fails) or their playful refusal to stay on task. In a game packed with infinite possibilities, what are GMs supposed to do when their players choose those for which they're not prepared? The Game Master’s Book of Random Encounters provides an unbeatable solution. This massive tome is divided into location categories, each of which can stand alone as a small stop as part of a larger campaign. As an example, the “Taverns, Inns, Shops & Guild Halls” section includes maps for 19 unique spaces, as well as multiple encounter tables designed to help GMs fill in the sights, sounds, smells and proprietors of a given location, allowing for each location in the book to be augmented and populated on the fly while still ensuring memorable moments for all your players. Each map is presented at scale on grid, enabling GMs to determine exactly where all of the characters are in relation to one another and anyone (or anything) else in the space, critical information should any combat or other movement-based action occur. Perhaps more useful than its nearly 100 maps, the book's one-shot generator features all the story hooks necessary for GMs to use these maps as part of an interconnected and contained adventure. Featuring eight unique campaign drivers that lead players through several of the book's provided maps, the random tables associated with each stage in the adventure allow for nearly three million different outcomes, making The Game Master's Book of Random Encounters an incredible investment for any would-be GM. The book also includes a Random NPC Generator to help you create intriguing characters your players will love (or love to hate), as well as a Party Makeup Maker for establishing connections among your PCs so you can weave together a disparate group of adventurers with just a few dice rolls. Locations include taverns, temples, inns, animal/creature lairs, gatehouses, courts, ships, laboratories and more, with adventure hooks that run the gamut from frantic rooftop chases to deep cellar dungeon-crawls, with a total of 97 maps, more than 150 tables and millions of possible adventures. No matter where your players end up, they'll have someone or something to persuade or deceive, impress or destroy. As always, the choice is theirs. But no matter what they choose, with The Game Master's Book of Random Encounters, you'll be ready.
Author: usenix International Middleware
Publisher: Springer Science & Business Media
ISBN: 3540234284
Category : Computers
Languages : en
Pages : 528
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Book Description
This book constitutes the refereed proceedings of the ACM/IFIP/USENIX International Conference on Distributed Systems Platforms, Middleware 2004, held in Toronto, Canada in October 2004. The 25 revised full papers presented together with an invited paper were carefully reviewed and selected from a total of 194 submissions. The papers are organized in topical sections on peer-to-peer computing; routing protocols and overlay; middleware for replication and overlay; middleware for replication and transactions; publish/subscribe systems; Web services: composition, integration, and interoperatibilty; middleware for mobility; application servers, enterprise computing, and software engineering.
Author: John A. Bissonette
Publisher: Springer Science & Business Media
ISBN: 1461219183
Category : Science
Languages : en
Pages : 419
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Book Description
While the research and management of wildlife has traditionally emphasised studies at smaller scales, it is now acknowledged that larger, landscape-level patterns strongly influence demographic processes in wild animal species. This book is the first to provide the conceptual basis for learning how larger scale patterns and processes can influence the biology and management of wildlife species. It is divided into three sections: Underlying Concepts, Landscape Metrics and Applications and Large Scale Management.
Author: D. Kannan
Publisher: CRC Press
ISBN: 1482294702
Category : Mathematics
Languages : en
Pages : 790
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Book Description
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Author: A. Katok
Publisher: Elsevier
ISBN: 0080478220
Category : Mathematics
Languages : en
Pages : 1235
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Book Description
This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Author: Arno Berger
Publisher: Princeton University Press
ISBN: 1400866588
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law’s colorful history, rapidly growing body of empirical evidence, and wide range of applications. An Introduction to Benford’s Law begins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the law, the book develops the significant-digit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benford’s law. Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The text includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significant-digit law. This text can serve as both a primary reference and a basis for seminars and courses.
Author: Brigitte Chauvin
Publisher: Birkhäuser
ISBN: 3034882114
Category : Mathematics
Languages : en
Pages : 526
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Book Description
This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science.
