000			a
999			_c30047 _d30047
008			200616b xxu||||| |||| 00| 0 eng d
020			_a9781107674424
082			_a511.5 _bBAR
100			_aBarlow, Martin T.
245			_aRandom walks and heat kernels on graphs
260			_bCambridge University Press _c2017 _aUnited Kingdom
300			_axi, 226 p. _c23 cm.
365			_b50.99 _cGBP _d98.20
490			_aLondon Mathematical Society lecture note series _v438
504			_aIncludes bibliographical references and index
520			_aThis 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 Poincaré 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.
650			_aGraph theory
650			_aHeat equation
650			_aMarkov processes
650			_aHeat kernel
650			_aElectrical resistance
942			_2ddc _cBK