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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.
The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this
The geographer Simon Küstenmacher collects exciting, entertaining and useful maps that open up a new perspective on the world in an extraordinary way.
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.
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.
"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
A highly visual exploration of diagrams and data that helps you understand how "maps" are part of everyday thinking, how they tell stories, and how they can reframe your point of view, from Stanford University's world-renowned d.school. “This book is the ultimate legend to mapping all kinds of data.”—Jessica Hagy, Webby Award-winning blogger of Indexed and author of How to Be Interesting (In Ten Simple Steps) Maps aren’t just geographic, they are also infographic and include all types of frameworks and diagrams. Any figure that sorts data visually and presents it spatially is a map. Maps are ways of organizing information and figuring out what’s important. Even stories can be mapped! The Secret Language of Maps provides a simple framework to deconstruct existing maps and then shows you how to create your own. An embedded mystery story about a woman who investigates the disappearance of an old high school friend illustrates how to use different maps to make sense of all types of information. Colorful illustrations bring the story to life and demonstrate how the fictional character’s collection of data, properly organized and “mapped,” leads her to solve the mystery of her friend’s disappearance. You’ll learn how to gather data, organize it, and present it to an audience. You’ll also learn how to view the many maps that swirl around our daily lives with a critical eye, aware of the forces that are in play for every creator.
This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.
Laugh and learn with fun facts about mapmakers, geography, compasses, and more—all told in Dr. Seuss’s beloved rhyming style and starring the Cat in the Hat! “You may travel the world, but no matter how far, with a map on your lap you will know where you are.” The Cat in the Hat’s Learning Library series combines beloved characters, engaging rhymes, and Seussian illustrations to introduce children to non-fiction topics from the real world! Go on a journey and learn: • how to read the latitude and longitude lines on a map • why a hiker uses a topographical map • why mapmakers use a scale and legends • and much more! Perfect for story time and for the youngest readers, There’s a Map on My Lap! All About Maps also includes an index, glossary, and suggestions for further learning. Look for more books in the Cat in the Hat’s Learning Library series! If I Ran the Horse Show: All About Horses Clam-I-Am! All About the Beach Miles and Miles of Reptiles: All About Reptiles A Whale of a Tale! All About Porpoises, Dolphins, and Whales Safari, So Good! All About African Wildlife Oh, the Lavas That Flow! All About Volcanoes Out of Sight Till Tonight! All About Nocturnal Animals What Cat Is That? All About Cats Once upon a Mastodon: All About Prehistoric Mammals Oh Say Can You Say What's the Weather Today? All About Weather The Cat on the Mat: All About Mindfulness
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