Introduction and Main Results

Abstract

In this introductory chapter, our problems and results are stated in such a fashion that a broad spectrum of readers could understand, and also described how these problems can be solved, using the mathematics presented in Chapters 2 through 4. In 1828, the English botanist R. Brown observed that pollen grains suspended in water move chaotically, incessantly changing their direction of motion. The physical explanation of this phenomenon is that a single grain suffers innumerable collisions with the randomly moving molecules of the surrounding water. A mathematical theory for Brownian motion was put forward by A. Einstein in 1905 ([Ei]). Einstein derived an accurate method of measuring Avogadro’s number by observing particles undergoing Brownian motion. Einstein’s theory was experimentally tested by J. Perrin between 1906 and