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The Lace Expansion And Its Applications

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The Lace Expansion And Its Applications

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Author : Gordon Slade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-17

The Lace Expansion And Its Applications written by Gordon Slade and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-17 with Mathematics categories.

The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models.

The Lace Expansion And Its Applications

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Author : Gordon Slade
language : en
Publisher: Springer
Release Date : 2006-08-29

The Lace Expansion And Its Applications written by Gordon Slade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Mathematics categories.

The Lace Expansion And Its Applications

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Author : Gordon Slade
language : en
Publisher:
Release Date : 2004

The Lace Expansion And Its Applications written by Gordon Slade and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

Analysis And Stochastics Of Growth Processes And Interface Models

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Author : Peter Mörters
language : en
Publisher: OUP Oxford
Release Date : 2008-07-24

Analysis And Stochastics Of Growth Processes And Interface Models written by Peter Mörters and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-24 with Mathematics categories.

This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.

Forward Backward Stochastic Differential Equations And Their Applications

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Author : Jin Ma
language : en
Publisher: Springer
Release Date : 2007-04-24

Forward Backward Stochastic Differential Equations And Their Applications written by Jin Ma and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-24 with Mathematics categories.

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Probability And Phase Transition

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Author : G.R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Probability And Phase Transition written by G.R. Grimmett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

The Analysis Of Fractional Differential Equations

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Author : Kai Diethelm
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-03

The Analysis Of Fractional Differential Equations written by Kai Diethelm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-03 with Mathematics categories.

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Polygons Polyominoes And Polycubes

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Author : A. J. Guttmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-18

Polygons Polyominoes And Polycubes written by A. J. Guttmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-18 with Science categories.

The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.

Surveys In Stochastic Processes

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Author : Jochen Blath
language : en
Publisher: European Mathematical Society
Release Date : 2011

Surveys In Stochastic Processes written by Jochen Blath and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume.

Some Mathematical Models From Population Genetics

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Author : Alison Etheridge
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-07

Some Mathematical Models From Population Genetics written by Alison Etheridge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-07 with Mathematics categories.

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

The Lace Expansion And Its Applications

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