Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability.

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry.

This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks.

The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject.

Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability.

Introduction Statement of the results Mixing time preliminaries Outline of the proof of Theorem 2.1 Random graph estimates Supercritical case Subcritical case Critical Case Fast mixing of the Swendsen-Wang process on trees Acknowledgements ...

This textbook covers all the essential elements of the theory of Brownian motion, a core area of probability theory, as well as the most recent research.