Two Dimensional Random Walk
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Two Dimensional Random Walk
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Author : Serguei Popov
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18
Two Dimensional Random Walk written by Serguei Popov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-18 with Mathematics categories.
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Principles Of Random Walk
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Author : Frank Spitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Principles Of Random Walk written by Frank Spitzer 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 2013-03-14 with Mathematics categories.
In this edition a large number of errors have been corrected, an occasional proof has been streamlined, and a number of references are made to recent pro gress. These references are to a supplementary bibliography, whose items are referred to as [S1] through [S26]. A thorough revision was not attempted. The development of the subject in the last decade would have required a treatment in a much more general con text. It is true that a number of interesting questions remain open in the concrete setting of random walk on the integers. (See [S 19] for a recent survey). On the other hand, much of the material of this book (foundations, fluctuation theory, renewal theorems) is now available in standard texts, e.g. Feller [S9], Breiman [S1], Chung [S4] in the more general setting of random walk on the real line. But the major new development since the first edition occurred in 1969, when D. Ornstein [S22] and C. J. Stone [S26] succeeded in extending the recurrent potential theory in· Chapters II and VII from the integers to the reals. By now there is an extensive and nearly complete potential theory of recurrent random walk on locally compact groups, Abelian ( [S20], [S25]) as well as non Abelian ( [S17], [S2] ). Finally, for the non-specialist there exists now an unsurpassed brief introduction to probabilistic potential theory, in the context of simple random walk and Brownian motion, by Dynkin and Yushkevich [S8].
Random Walks And Electric Networks
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Author : Peter G. Doyle
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Random Walks And Electric Networks written by Peter G. Doyle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Electric network topology categories.
Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Stopped Random Walks
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stopped Random Walks written by Allan Gut 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 Mathematics categories.
My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words.
Random Walks In Biology
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Author : Howard C. Berg
language : en
Publisher: Princeton University Press
Release Date : 2025-10-28
Random Walks In Biology written by Howard C. Berg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-10-28 with Science categories.
A landmark account of the dynamics of living systems and the methods for studying them Random Walks in Biology provides a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. Howard Berg offers an essential foundation for understanding random motions of molecules, subcellular particles, and cells as well as the processes that are affected by such motions. Using the concept of “random walks” of individual particles, Berg illuminates the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility. With an engaging foreword by theoretical biophysicist William Bialek, this Princeton Science Library edition can serve as a supplementary text for courses on biochemistry, molecular biology, biomechanics, physiology, biophysics, and physical chemistry. It is also an ideal reference volume.
Intermediate Physics For Medicine And Biology
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Author : Russell K. Hobbie
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-09
Intermediate Physics For Medicine And Biology written by Russell K. Hobbie 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 2007-09-09 with Science categories.
This text bridges the gap between introductory physics and its application to the life sciences. It is intended for advanced undergraduates and beginning graduate students. The Fourth Edition is updated to include new findings, discussion of stochastic processes and expanded coverage of anatomy and biology. The text includes many problems to test the student's understanding, and chapters include useful bibliographies for further reading. Its minimal prerequisites and wide coverage make it ideal for self-study. The fourth edition is updated throughout to reflect new developments.
Trends In Probability And Related Analysis Proceedings Of Sap 98
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Author : N Kono
language : en
Publisher: World Scientific
Release Date : 1999-10-19
Trends In Probability And Related Analysis Proceedings Of Sap 98 written by N Kono and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-19 with categories.
This proceedings volume reflects the current interest in and future direction of probability theory and related theory of analysis and statistics. It contains 2 survey papers and 21 contributed papers.
Cellular Automaton Modeling Of Biological Pattern Formation
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Author : Andreas Deutsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-26
Cellular Automaton Modeling Of Biological Pattern Formation written by Andreas Deutsch 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 2007-12-26 with Science categories.
This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models. While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling.
Advances In Combinatorial Methods And Applications To Probability And Statistics
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Author : N. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Combinatorial Methods And Applications To Probability And Statistics written by N. Balakrishnan 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 2012-12-06 with Mathematics categories.
Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
Random Walk And The Heat Equation
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-11-22
Random Walk And The Heat Equation written by Gregory F. Lawler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Mathematics categories.
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.