Customer Reviews:
 Excellent January 14, 2007
This book is a real and rare gem of mathematical teaching. It explains in easy and accessible language the links between the topics in the title with remarkable clarity and simplicity. Of course the real strength of a book like this is to show to beginner mathematicians the power one can acquire by looking at a given problem from several perspectives, and this is where the book really excels.
The authors are doing a great job in reducing all concepts to the essential, but never - on the other side - trivializing or leaving essential things unexplained. College algebra is all what is required to understand it, and you will certainly be rewarded.
Relationship between Random Walks and Electric Networks! January 27, 2002
3 out of 3 found this review helpful
The book brings together two of my passions : random
walks and electric networks. It turns out that there are
interesting relationships between these two areas, so insights
in one provide can be used to prove things in the other.There is this beautiful theorem by Polya which states that a
random walker on an infinite street network in d-dimensional
space is bound to return to the starting point when d = 2,
but has a positive probability of escaping to infinity without
returning to the starting point when d >= 3. The book
reinterprets this theorem as a statement about electric networks,
and then proves the theorem using techniques from classical
network theory. The proof relies on showing that the resistance
of the corresponding electric network in 1 and 2 dimensions
is infinite, whereas it is finite in the 3 dimensional case.
Thus some current [like our random walker] can flow to infinity. Strongly recommended!. Also check out Peter Doyle's webpage
at Dartmouth "http://math.dartmouth.edu/~doyle/"
Relationship between Random Walks and Electric Networks! January 27, 2002
4 out of 4 found this review helpful
The book brings together two of my passions : random
walks and electric networks. It turns out that there are
interesting relationships between these two areas, so insights
in one can be used to prove things in the other.There is this beautiful theorem by Polya which states that a
random walker on an infinite street network in d-dimensional
space is bound to return to the starting point when d = 2,
but has a positive probability of escaping to infinity without
returning to the starting point when d >= 3. The book
reinterprets this theorem as a statement about electric networks,
and then proves the theorem using techniques from classical
network theory. The proof relies on showing that the resistance
of the corresponding electric network in 1 and 2 dimensions
is infinite, whereas it is finite in the 3 dimensional case.
Thus some current [like our random walker] can flow to infinity. Strongly recommended!.
cool analogies April 1, 2001
This book provides fascinating insights and analogies between random walks and electric networks- and how you can exploit these analogies to solve difficult problems in one using the other... there's also a nice proof of the "Polya's theorem" using these analogies- basically Polya's theorem says that a random walk in dimensions >2 is transient, while a random walk on a plane or a line always returns to its starting point...
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