Chapter 1. Probability elements

1.1 Introduction to random variables

1.2 Axiomatic scheme

1.2.1 Conditional probability

1.2.2 Bayes' theorem

1.2.3 Statistical Independence

1.3 Frequency scheme

1.3.1 Probability density

1.3.2 Properties of the probability density

1.4 Characteristic function G(k)

1.4.1 The simplest of random walks

1.4.3 Characteristic function in a toroidal network

1.4.4 Function of characteristic function

1.5 Cumulants development

1.6 Central limit theorem

1.7 Random variable transformation

1.8 Correlations between random variables

1.9 Fluctuations development

1.10 Multidimensional characteristic function

1.10.1 Diagrams development (many variables)

1.11 Terwiel cumulants

1.12 Gaussian distribution (many variables)

1.12.2 Novikov's theorem

1.13 Transformation for n dimensional probability densities

1.13.1 Marginal probability density

1.14 Conditional probability density

1.15 Problems and solutions

Chapter 2. Fluctuations around thermal equilibrium

2.1 Spatial correlations (Einstein's distribution)

2.1.1 The Gaussian approximation

2.2 Minimal work

2.2.1 Fluctuations in terms of P, V, T variables

2.3 Fluctuations of mechanical character

2.3.1 Fluctuations of a tight rope

2.5 Problems and solutions

Chapter 3. Elements of stochastic processes

3.1 Introduction

3.1.1 Time dependent random variable

3.1.2 Characteristic fun
About the Author:

Prof. Dr. Manuel Osvaldo Caceres did his PhD in Physics, in anomalous transport in heterogeneous media in 1986 at the Instituto Balseiro, Argentina. He had several Post-Doc stays in Spain, Germany and Belgium, therefore getting himself into the new trends of non-equilibrium statistical mechanics. His main contributions were in: dynamical localization, nonlinear optics, stochastic liquid crystals, pattern formation in fluids, and explosive systems. In 2005, he got an Associate Professor position at the International Center of Theoretical Physics (ICTP), Trieste, Italy, after which he returned to his country to teach non-equilibrium statistical mechanics and disorder.

Dr. Manuel O. Caceres is currently Full Professor at the Instituto Balseiro, Univ. Nac. Cuyo, Argentina. Senior Researcher at Centro Atómico Bariloche, Comisión Nacional de Energía Atómica (CNEA), Argentina. Former Head of the Statistical Division at the Centro Atomico Bariloche, CNEA, Argentina.

He has published more than a hundred of peer reviewed papers in international journals in the fields of anomalous transport in solid state physics, diffusion-advection in random fluids, pattern formation in stochastic Rayleigh-Bénard experiments, phenomenology in quantum dissipation, and theory of extreme densities in random media. He also published a textbook on statistical non-equilibrium mechanics and random media, in Spanish.