The main aim of this book is to reveal connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies heat diffusion at this general level and discusses the multiplicative Einstein relation; Isoperimetric inequalities; and Heat kernel estimates; Elliptic and parabolic Harnack inequality.
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From the reviews:
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. ... The book is intended to be self-contained and accessible to graduate and Ph.D. students. It contains a wealth of references, also on various aspects of random walks not covered by the text." (Wolfgang König, Mathematical Reviews, Issue 2007 d)
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. ... The book is intended to be self-contained and accessible to graduate and PhD students. It contains a wealth of references, also on various aspects of random walks not covered by the text. At the end of the book a list of some dozens of types of inequalities appear that are introduced in the book" (Wolfgang König, Zentralblatt MATH, Vol. 1104 (6), 2007)
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. ... The book is intended to be self-contained and accessible to graduate and Ph.D. students. It contains a wealth of references, also on various aspects of random walks not covered by the text." (Wolfgang König, Mathematical Reviews, Issue 2007 d)
"This book studies random walks on countable infinite connected weighted graphs, with particular emphasis on fractal graphs like the Sierpinski triangular graph or the weighted Vicsek tree. ... The book is intended to be self-contained and accessible to graduate and PhD students. It contains a wealth of references, also on various aspects of random walks not covered by the text. At the end of the book a list of some dozens of types of inequalities appear that are introduced in the book" (Wolfgang König, Zentralblatt MATH, Vol. 1104 (6), 2007)