## Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons

*Stefan Adams*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0007
- Subject:
- Mathematics, Probability / Statistics, Analysis

Motivated by the Bose gas, this chapter introduces certain combinatorial structures. It analyses the asymptotic behaviour of empirical shape measures and of empirical path measures of N Brownian ... More

## Science’s Cinematic Method: Motion Pictures and Scientific Research

*Scott Curtis*

### in The Shape of Spectatorship: Art, Science, and Early Cinema in Germany

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780231134033
- eISBN:
- 9780231508636
- Item type:
- chapter

- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231134033.003.0002
- Subject:
- Film, Television and Radio, Film

Chapter One examines use of film as a scientific research tool in three fields (human motion studies, physics, biology) in Germany from the 1880s to 1914. It argues that there is a close relationship ... More

## Random Fractals

*Peter Mörters*

### in New Perspectives in Stochastic Geometry

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232574
- eISBN:
- 9780191716393
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232574.003.0008
- Subject:
- Mathematics, Geometry / Topology

This chapter expounds the theory of random fractals, using tree representation as a unifying principle. Applications to the fine structure of Brownian motion are discussed.

## Interacting Brownian Motions and the Gross-Pitaevskii Formula

*Stefan Adams and Wolfgang König*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0008
- Subject:
- Mathematics, Probability / Statistics, Analysis

Bose–Einstein condensation predicts that, under certain conditions (in particular extremely low temperature), all particles will condense into one state. Some of the physical background is surveyed ... More

## Brownian motions on groups of matrices

*Jacques Franchi and Yves Le Jan*

### in Hyperbolic Dynamics and Brownian Motion: An Introduction

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199654109
- eISBN:
- 9780191745676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199654109.003.0007
- Subject:
- Mathematics, Mathematical Physics

This chapter is devoted to (left and right) Brownian motions on groups of matrices, which the chapter constructs as solutions to linear stochastic differential equations. The chapter establishes in ... More

## Evidence for Molecules: Jean Perrin and Molecular Reality

*Peter Achinstein*

### in The Book of Evidence

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195143898
- eISBN:
- 9780199833023
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195143892.003.0012
- Subject:
- Philosophy, Philosophy of Science

Jean Perrin's argument for the existence of molecules on the basis of his 1908 experiments with Brownian motion is examined. Various interpretations of that argument, including hypothetico‐deductive, ... More

## Stochastic Processes and Stochastic Calculus

*Claus Munk*

### in Fixed Income Modelling

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199575084
- eISBN:
- 9780191728648
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575084.003.0003
- Subject:
- Economics and Finance, Financial Economics

The price of an asset at a future point in time will typically be unknown, i.e. a random variable. In order to describe the uncertain evolution in the price of the asset over time, we need a ... More

## Quantum Master Equations

*Heinz-Peter Breuer and Francesco Petruccione*

### in The Theory of Open Quantum Systems

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199213900
- eISBN:
- 9780191706349
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213900.003.03
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the fundamentals of the description of the quantum dynamics of open systems in terms of quantum master equations, together with its most important applications. Special ... More

## Brownian Motion: Fluctuations, Dynamics, and Applications

*Robert M. Mazo*

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199556441
- eISBN:
- 9780191705625
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556441.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

Brownian motion is the incessant motion of small particles immersed in an ambient medium. It is due to fluctuations in the motion of the medium particles on the molecular scale. The name has been ... More

## Uncertainty, Information, and Stochastic Processes

*Claus Munk*

### in Financial Asset Pricing Theory

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199585496
- eISBN:
- 9780191751790
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199585496.003.0002
- Subject:
- Economics and Finance, Econometrics

Uncertainty is a key component of financial markets and thus of any asset pricing theory. This chapter provides the tools from probability theory that are being used in the asset pricing models ... More

## Brownian Motion

*Gopinath Kallianpur and P. Sundar*

### in Stochastic Analysis and Diffusion Processes

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199657063
- eISBN:
- 9780191781759
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199657063.003.0002
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

After defining a Brownian motion (also known as a Wiener process), a standard one-dimensional Brownian motion is constructed by the use of Haar functions. Properties of a Brownian motion such as ... More

## Brownian Motion in Granular Gases

*Nikolai V. Brilliantov and Thorsten Pöschel*

### in Kinetic Theory of Granular Gases

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0015
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter analyzes Brownian motion in granular gases. Topics discusses include Boltzmann equation for the velocity distribution function of Brownian particles, Fokker–Planck equation for Brownian ... More

## Kinetic Theory of Granular Gases

*Nikolai V. Brilliantov and Thorsten Pöschel*

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ... More

## Weak Convergence in a Function Space

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0027
- Subject:
- Economics and Finance, Econometrics

This chapter applies the theory of Ch. 26 to the case of the space C of continuous functions on the unit interval. It is shown how to assign probability measures to C, and Weiner measure (Brownian ... More

## Hyperbolic Dynamics and Brownian Motion: An Introduction

*Jacques Franchi and Yves Le Jan*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199654109
- eISBN:
- 9780191745676
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199654109.001.0001
- Subject:
- Mathematics, Mathematical Physics

The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) ... More

## Brownian Motion and Stochastic Calculus

*Kerry E. Back*

### in Asset Pricing and Portfolio Choice Theory

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190241148
- eISBN:
- 9780190241179
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190241148.003.0012
- Subject:
- Economics and Finance, Financial Economics

Brownian motion and concepts of the Itôs calculus are explained, including total variation, quadratic variation, Levy’s characterization of Brownian motion, the Itô integral, the difference between ... More

## Brownian Motion

*Phil Attard*

### in Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199662760
- eISBN:
- 9780191745287
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662760.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

Brownian motion is presented as a stochastic process, and as a bridge between thermodynamics and statistical mechanics. Einstein’s result for the linear growth in time of the mean square displacement ... More

## The Theory of Open Quantum Systems

*Heinz-Peter Breuer and Francesco Petruccione*

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199213900
- eISBN:
- 9780191706349
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213900.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a ... More

## Basic Itô calculus

*Jacques Franchi and Yves Le Jan*

### in Hyperbolic Dynamics and Brownian Motion: An Introduction

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199654109
- eISBN:
- 9780191745676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199654109.003.0006
- Subject:
- Mathematics, Mathematical Physics

This chapter deals with the basic Itô calculus. Fundamental notions such as predictability, martingales and stopping times are introduced in the discrete case. The chapter then gives a short account ... More

## Examples of Markovian processes

*Melvin Lax, Wei Cai, and Min Xu*

### in Random Processes in Physics and Finance

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567769
- eISBN:
- 9780191718359
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567769.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Consider two physical problems describable by the same random process. The first process is the radioactive decay of a collection of nuclei. The second is the production of photoelectrons by a steady ... More