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## 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

## 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

## Directed Random Growth Models on the Plane

*Timo Seppäläinen*

### 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/9780199239252.003.0001
- Subject:
- Mathematics, Probability / Statistics, Analysis

This chapter discusses random growth models describing the evolution of an interface in the plane. For specific models, three basic questions are discussed. First, under appropriate scaling, what is ... More

## Introduction to Large Deviation Theory

*M. Vidyasagar*

### in Hidden Markov Processes: Theory and Applications to Biology

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0005
- Subject:
- Mathematics, Probability / Statistics

This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct ... More

## PERCOLATION AND THE LARGEST COMPONENT

*Mathew Penrose*

### in Random Geometric Graphs

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0010
- Subject:
- Mathematics, Probability / Statistics

This chapter concerns the largest component of G(N(n),r) in the thermodynamic limit when the number of points N(n) is Poisson with parameter n and the underlying density is uniform on the unit ... More

## Nucleation and Droplet Growth as a Stochastic Process

*Oliver Penrose*

### 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/9780199239252.003.0012
- Subject:
- Mathematics, Probability / Statistics, Analysis

This chapter proposes a stochastic differential equation as the putative limit for a birth-and-death Markov chain model for the fluctuating size of a droplet, in a fluid, that is metastable with ... More

## INTRODUCTION

*Mathew Penrose*

### in Random Geometric Graphs

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0001
- Subject:
- Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More

## A probabilistic toolbox

*Marc Mézard and Andrea Montanari*

### in Information, Physics, and Computation

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780198570837
- eISBN:
- 9780191718755
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570837.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The three fields that form the subject of this book all deal with large sets of random variables. Not surprisingly, they possess common underlying structures and techniques. This chapter describes ... More

## Large Deviations Principle for Diffusions

*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/9780199657063.003.0012
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

Large deviations theory formulated by Varadhan has made a tremendous impact in a variety of fields such as mathematical physics, control theory, and statistics, to name a few. After a brief ... More

## Stochastic Analysis and Diffusion Processes

*Gopinath Kallianpur and P Sundar*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199657063.001.0001
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local ... More

## The Large Deviations Method and Its Applications

*A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo*

### in Physics of Long-Range Interacting Systems

- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780199581931
- eISBN:
- 9780191787140
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581931.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter is devoted to the study of a very useful mathematical tool for the computation of the entropy in long-range systems. The method is based on large deviation theory, and it is very well ... More

## Wave–Particles Interaction

*A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo*

### in Physics of Long-Range Interacting Systems

- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780199581931
- eISBN:
- 9780191787140
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581931.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this Chapter an alternative derivation of the self-consistent Vlasov-Maxwell equations for wave-particles interaction is given. The analysis is carried out under a rigorous Hamiltonian framework ... More

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