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Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis
  • Language: en
  • Pages: 114

Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis

Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.

Spatial Fleming-Viot Models with Selection and Mutation
  • Language: en
  • Pages: 866

Spatial Fleming-Viot Models with Selection and Mutation

  • Type: Book
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  • Published: 2013-12-12
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  • Publisher: Springer

This book constructs a rigorous framework for analysing selected phenomena in evolutionary theory of populations arising due to the combined effects of migration, selection and mutation in a spatial stochastic population model, namely the evolution towards fitter and fitter types through punctuated equilibria. The discussion is based on a number of new methods, in particular multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measure-valued evolutions and new forms of duality (for state-dependent mutation and multitype selection) which are used to prove ergodic theorems in this context and are applicable for many other questions and renormalization analysis for a variety of phenomena (stasis, punctuated equilibrium, failure of naive branching approximations, biodiversity) which occur due to the combination of rare mutation, mutation, resampling, migration and selection and make it necessary to mathematically bridge the gap (in the limit) between time and space scales.

Coupling and Harmonic Functions in the Case of Continuous Time Markov Processes
  • Language: en
  • Pages: 80
Interacting Stochastic Systems
  • Language: en
  • Pages: 470

Interacting Stochastic Systems

The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences.

Interacting Stochastic Systems
  • Language: en
  • Pages: 443

Interacting Stochastic Systems

Core papers emanating from the research network, DFG-Schwerpunkt: Interacting stochastic systems of high complexity.

Entropy
  • Language: en
  • Pages: 376

Entropy

The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of m...

Queering the Countryside
  • Language: en
  • Pages: 404

Queering the Countryside

  • Type: Book
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  • Published: 2016-03-15
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  • Publisher: NYU Press

"This collection of original essays confronts the assumption that queer desires depend upon urban life for meaning. By considering rural queer life, the contributors challenge readers to explore queer experiences in ways that give greater context and texture to modern practices of identity formation. The book's focus on understudied rural spaces throws into relief the overemphasis of urban locations and structures in the current political and theoretical work on queer sexualities and genders. It highlights the need to rethink notions of 'the closet' and 'coming out' and the characterizations of non-urban sexualities and genders as 'isolated' and in need of 'outreach'"--Provided by publisher.

Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems
  • Language: en
  • Pages: 260

Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems

The papers in this collection explore the connections between the rapidly developing fields of measure-valued processes, stochastic partial differential equations, and interacting particle systems, each of which has undergone profound development in recent years. Bringing together ideas and tools arising from these different sources, the papers include contributions to major directions of research in these fields, explore the interface between them, and describe newly developing research problems and methodologies. Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these processes are described, including br...

Probability in Complex Physical Systems
  • Language: en
  • Pages: 518

Probability in Complex Physical Systems

Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.