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
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.
This note covers the following topics: Rigidity and inflexibility in conformal dynamics, Hausdorff
dimension and conformal dynamics: Strong convergence of Kleinian groups,
Geometrically finite rational maps and Computation of dimension.