Functional Gaussian Approximation For Dependent Structures
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Functional Gaussian Approximation For Dependent Structures
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Author : Florence Merlevède
language : en
Publisher: Oxford University Press
Release Date : 2019-02-14
Functional Gaussian Approximation For Dependent Structures written by Florence Merlevède and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.
High Dimensional Probability Ix
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Author : Radosław Adamczak
language : en
Publisher: Springer Nature
Release Date : 2023-06-05
High Dimensional Probability Ix written by Radosław Adamczak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-05 with Mathematics categories.
This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
Local Limit Theorems For Inhomogeneous Markov Chains
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Author : Dmitry Dolgopyat
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Local Limit Theorems For Inhomogeneous Markov Chains written by Dmitry Dolgopyat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
High Dimensional Probability Viii
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Author : Nathael Gozlan
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
High Dimensional Probability Viii written by Nathael Gozlan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
This volume collects selected papers from the 8th High Dimensional Probability meeting held at Casa Matemática Oaxaca (CMO), Mexico. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, random graphs, information theory and convex geometry. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.
Supramolecular Structure And Function 10
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Author : Jasminka Brnjas-Kraljević
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-22
Supramolecular Structure And Function 10 written by Jasminka Brnjas-Kraljević 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 2011-03-22 with Medical categories.
The book is based on lectures presented on the International Summer School on Biophysics held in Croatia in September 2009. The advantage of the School is that it provides advanced training in very broad scope of areas related to biophysics contrary to other similar schools or workshops that are centered mainly on one topic or technique. In this volume, tenth in the row, the papers in the field of biophysics are presented. The topics are biological phenomena from single protein to macromolecular aggregations structure by using variant physical methods (NMR, EPR, FTIR, Mass Spectrometry, etc.). The interrelationship of supramolecular structures and their functions is enlightened by applications of principals of these physical methods in the biophysical and molecular biology context.
Advances In Time Dependent Methods For Nuclear Structure And Dynamics
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Author : Paul Denis Stevenson
language : en
Publisher: Frontiers Media SA
Release Date : 2021-03-08
Advances In Time Dependent Methods For Nuclear Structure And Dynamics written by Paul Denis Stevenson and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-08 with Science categories.
Statistical Physics Of Liquids At Freezing And Beyond
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Author : Shankar Prasad Das
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-16
Statistical Physics Of Liquids At Freezing And Beyond written by Shankar Prasad Das 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 2011-06-16 with Science categories.
Exploring important theories for understanding freezing and the liquid-glass transition, this book is useful for graduate students and researchers in soft-condensed matter physics, chemical physics and materials science. It details recent ideas and key developments, providing an up-to-date view of current understanding. The standard tools of statistical physics for the dense liquid state are covered. The freezing transition is described from the classical density functional approach. Classical nucleation theory as well as applications of density functional methods for nucleation of crystals from the melt are discussed, and compared to results from computer simulation of simple systems. Discussions of supercooled liquids form a major part of the book. Theories of slow dynamics and the dynamical heterogeneities of the glassy state are presented, as well as nonequilibrium dynamics and thermodynamic phase transitions at deep supercooling. Mathematical treatments are given in full detail so readers can learn the basic techniques.
Conceptual Density Functional Theory And Its Application In The Chemical Domain
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Author : Nazmul Islam
language : en
Publisher: CRC Press
Release Date : 2018-06-13
Conceptual Density Functional Theory And Its Application In The Chemical Domain written by Nazmul Islam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Mathematics categories.
In this book, new developments based on conceptual density functional theory (CDFT) and its applications in chemistry are discussed. It also includes discussion of some applications in corrosion and conductivity and synthesis studies based on CDFT. The electronic structure principles—such as the electronegativity equalization principle, the hardness equalization principle, the electrophilicity equalization principle, and the nucleophilicity equalization principle, along studies based on these electronic structure principles—are broadly explained. In recent years some novel methodologies have been developed in the field of CDFT. These methodologies have been used to explore mutual relationships between the descriptors of CDFT, namely electronegativity, hardness, etc. The mutual relationship between the electronegativity and the hardness depend on the electronic configuration of the neutral atomic species. The volume attempts to cover almost all such methodology. Conceptual Density Function Theory and Its Application in the Chemical Domain will be an appropriate guide for research students as well as the supervisors in PhD programs. It will also be valuable resource for inorganic chemists, physical chemists, and quantum chemists. The reviews, research articles, short communications, etc., covered by this book will be appreciated by theoreticians as well as experimentalists.
Electronic Structure Calculations For Solids And Molecules
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Author : Jorge Kohanoff
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-29
Electronic Structure Calculations For Solids And Molecules written by Jorge Kohanoff 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 2006-06-29 with Science categories.
Electronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.
Time Dependent Density Functional Theory
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Author : Carsten Ullrich
language : en
Publisher: Oxford University Press
Release Date : 2012
Time Dependent Density Functional Theory written by Carsten Ullrich and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Science categories.
Time-dependent density-functional theory (TDDFT) is a quantum mechanical approach for the dynamical properties of electrons in matter. It's widely used in (bio)chemistry and physics to calculate molecular excitation energies and optical properties of materials. This is the first graduate-level text on the formal framework and applications of TDDFT.