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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Random Walks and Heat Kernels on Graphs (Paperback)
Loot Price: R1,682
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Random Walks and Heat Kernels on Graphs (Paperback)
Series: London Mathematical Society Lecture Note Series
Expected to ship within 12 - 17 working days
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This introduction to random walks on infinite graphs gives
particular emphasis to graphs with polynomial volume growth. It
offers an overview of analytic methods, starting with the
connection between random walks and electrical resistance, and then
proceeding to study the use of isoperimetric and Poincare
inequalities. The book presents rough isometries and looks at the
properties of a graph that are stable under these transformations.
Applications include the 'type problem': determining whether a
graph is transient or recurrent. The final chapters show how
geometric properties of the graph can be used to establish heat
kernel bounds, that is, bounds on the transition probabilities of
the random walk, and it is proved that Gaussian bounds hold for
graphs that are roughly isometric to Euclidean space. Aimed at
graduate students in mathematics, the book is also useful for
researchers as a reference for results that are hard to find
elsewhere.
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