In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications.

Author: Abram Skogseid

Publisher: Nova Science Pub Incorporated

ISBN: 1614709661

Category: Mathematics

Page: 651

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In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny.

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work.

Author: Vladas Sidoravicius

Publisher: Springer Nature

ISBN: 9789811503023

Category: Mathematics

Page: 341

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Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Random Walks in Finance and Physics The Introduction, Chap. 1, suggested that there is a resemblance of financial price histories to a random walk. It is therefore more than a simple curiosity that the first successful theory of the ...

Author: Johannes Voit

Publisher: Springer Science & Business Media

ISBN: 9783662044230

Category: Science

Page: 220

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A careful examination of the interaction between physics and finance. It takes a look at the 100-year-long history of co-operation between the two fields and goes on to provide new research results on capital markets - taken from the field of statistical physics. The random walk model, well known in physics, is one good example of where the two disciplines meet. In the world of finance it is the basic model upon which the Black-Scholes theory of option pricing and hedging has been built. The underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated.

In this chapter, we will explore the emergent behavior for random walks. Random walks are paths that take successive steps in random directions. They arise often in statistical mechanics: as partial sums of fluctuating quantities, ...

Author: James Sethna

Publisher: Oxford University Press

ISBN: 9780198566762

Category: Computers

Page: 372

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Sethna distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, and modern biology. He explores everything from chaos through to life at the end of the universe.

In this chapter we will explore the emergent behavior for random 2.4 Solving the diffusion equation walks . Random walks are paths that take successive steps in random 30 directions . They arise often in statistical mechanics : as ...

Author: James P. Sethna

Publisher: Oxford University Press

ISBN: 9780192634535

Category: Science

Page: 400

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Statistical mechanics is our tool for deriving the laws that emerge from complex systems. Sethna's text distills the subject to be accessible to those in all realms of science and engineering — avoiding extensive use of quantum mechanics, thermodynamics, and molecular physics. Statistical mechanics explains how bacteria search for food, and how DNA replication is proof-read in biology; optimizes data compression, and explains transitions in complexity in computer science; explains the onset of chaos, and launched random matrix theory in mathematics; addresses extreme events in engineering; and models pandemics and language usage in the social sciences. Sethna's exercises introduce physicists to these triumphs and a hundred others — broadening the horizons of scholars both practicing and nascent. Flipped classrooms and remote learning can now rely on 33 pre-class exercises that test reading comprehension (Emergent vs. fundamental; Weirdness in high dimensions; Aging, entropy and DNA), and 70 in-class activities that illuminate and broaden knowledge (Card shuffling; Human correlations; Crackling noises). Science is awash in information, providing ready access to definitions, explanations, and pedagogy. Sethna's text focuses on the tools we use to create new laws, and on the fascinating simple behavior in complex systems that statistical mechanics explains.

Volume 91, 2016 http://dx.doi.org/10.1090/pspum/091/01540 Random walk problems motivated by statistical physics Gregory F. Lawler This paper is dedicated to the memory of Ed Nelson. Abstract. This paper is an expanded version of a talk ...

Author: V. Sidoravicius

Publisher: American Mathematical Soc.

ISBN: 9781470422486

Category: Combinatorial analysis

Page: 471

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This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.

With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic ...

Author: Gregory F. Lawler

Publisher: Birkhäuser

ISBN: 1461459710

Category: Mathematics

Page: 223

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A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The present softcover reprint includes corrections and addenda from the 1996 printing, and makes this classic monograph available to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.

Exercise 2.4 The integral order Bessel functions satisfy e ( z − 1 / z ) p / 2 = Σ Jn ( p ) z " Show that Jn ( p ) = 2π N = 1∞ • π ei ( p sin 0 ― n0 ) de Statistical mechanics : the generating function as the ultimate goal of an ...

Author: Joseph Rudnick

Publisher: Cambridge University Press

ISBN: 113945014X

Category: Science

Page: 350

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Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

In this guide we will treat two fundamental problems in statistical mechanics with the simple sampling method. The first is the random walk and other problems of such type. The random walk problem should not be underestimated because of ...

Author: Kurt Binder

Publisher: Springer Science & Business Media

ISBN: 9783662088548

Category: Science

Page: 129

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When leaming very formal material one comes to a stage where one thinks one has understood the material. Confronted with a "reallife" problem, the passivity of this understanding sometimes becomes painfully elear. To be able to solve the problem, ideas, methods, etc. need to be ready at hand. They must be mastered (become active knowledge) in order to employ them successfully. Starting from this idea, the leitmotif, or aim, of this book has been to elose this gap as much as possible. How can this be done? The material presented here was born out of a series of lectures at the Summer School held at Figueira da Foz (Portugal) in 1987. The series of lectures was split into two concurrent parts. In one part the "formal material" was presented. Since the background of those attending varied widely, the presentation of the formal material was kept as pedagogic as possible. In the formal part the general ideas behind the Monte Carlo method were developed. The Monte Carlo method has now found widespread appli cation in many branches of science such as physics, chemistry, and biology. Because of this, the scope of the lectures had to be narrowed down. We could not give a complete account and restricted the treatment to the ap plication of the Monte Carlo method to the physics of phase transitions. Here particular emphasis is placed on finite-size effects.

Chapter 10 TRANSIENT RANDOM WALKS ON DYNAMICALLY ORIENTED LATTICES 1. INTRODUCTION The use of random walks as a tool in mathematical physics is now well established and they have been for example widely used in classical statistical ...

Author: Nadine Guillotin-Plantard

Publisher: Elsevier

ISBN: 0080462847

Category: Mathematics

Page: 278

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The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!). · New probabilistic model, new results in probability theory · Original applications in computer science · Applications in mathematical physics · Applications in finance