01971cam a22002298i 4500999001900000008004100019020001800060082001600078100002600094245004500120260005300165300001500218490005800233504005100291520109100342650003901433650002501472650002901497650002601526942001201552952017701564 c208859d208859161107s2017 enk b 001 0 eng a9781107674424 a511.5bB2R2 aBarlow, M. T.9359632 aRandom walks and heat kernels on graphs aUnited KingdombCambridge University Pressc2017 axi, 226 p. aLondon Mathematical Society lecture note series : 438 aIncludes bibliographical references and index. 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.
https://www.cambridge.org/core/books/random-walks-and-heat-kernels-on-graphs/5B375D343025BCE91C682D49CDDB3A1A#fndtn-information aRandom walks - Mathematics9359633 aGraph theory9359634 aMarkov processes9359635 aHeat equation9359636 2ddccBK 00102ddc406511_500000000000000_B2R2708NFIC9352134aVSLbVSLcGENd2018-03-07e12g3728.00kSlot 1356 (0 Floor, East Wing)o511.5 B2R2p196392r2018-03-07v4660.00yBK