This PDF book covers the following
topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff
dimensions, Self-similarity and packing dimension, Frostman’s theory and
capacity, Self-affine sets, Graphs of continuous functions, Brownian motion,
Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling
Salesman Theorem.
Author(s): Christopher J. Bishop Stony Brook
University, Yuval Peres Microsoft Research
This PDF book covers the following
topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff
dimensions, Self-similarity and packing dimension, Frostman’s theory and
capacity, Self-affine sets, Graphs of continuous functions, Brownian motion,
Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling
Salesman Theorem.
Author(s): Christopher J. Bishop Stony Brook
University, Yuval Peres Microsoft Research
The term fractal
usually refers to sets which, in some sense, have a self-similar structure. This
PDF book covers the following topics related to Random Fractals : Representing
fractals by trees, Fine properties of stochastic processes, More on the planar
Brownian path, etc.
Goal of this course
note is primarily to develop the foundations of geometric measure theory, and
covers in detail a variety of classical subjects. A secondary goal is to
demonstrate some applications and interactions with dynamics and metric number
theory.