Statistical Background

Abstract

For many interesting physical problems, we need to describe the “long-term” behavior of systems governed by macroscopic laws and microscopic randomness. A random event has an outcome that is uncertain and unpredictable. Sometimes small changes in initial conditions can result in a substantially different outcome – this is the essence of chaos. Quantities that change randomly in time and space are called stochastic processes. Physical systems that are subject to stochastic driving will have a random component and the variables that describe the system are also stochastic processes. Examples of physical problems include the behavior of gases in the presence of microscopic collisions of the constituent particles, the collective propagation of energetic charged particles in a magnetically turbulent medium, the collective behavior of dust particles in an accretion disk subject to coagulation and destruction, the evolution of a gas of charged protons and electrons (a plasma), etc.