Random Walks on Infinite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Infinite Groups write by Steven P. Lalley. This book was released on 2023-05-08. Random Walks on Infinite Groups available in PDF, EPUB and Kindle. This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
Random Walks on Infinite Graphs and Groups
Random Walks on Infinite Graphs and Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Infinite Graphs and Groups write by Wolfgang Woess. This book was released on 2000-02-13. Random Walks on Infinite Graphs and Groups available in PDF, EPUB and Kindle. The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Random walks on infinite graphs and groups
Random walks on infinite graphs and groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random walks on infinite graphs and groups write by Wolfgang Woess. This book was released on 1991. Random walks on infinite graphs and groups available in PDF, EPUB and Kindle.
Random Walks on Reductive Groups
Random Walks on Reductive Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Reductive Groups write by Yves Benoist. This book was released on 2016-10-20. Random Walks on Reductive Groups available in PDF, EPUB and Kindle. The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Boundaries and Random Walks on Finitely Generated Infinite Groups
Boundaries and Random Walks on Finitely Generated Infinite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Boundaries and Random Walks on Finitely Generated Infinite Groups write by Anders Karlsson. This book was released on 2001. Boundaries and Random Walks on Finitely Generated Infinite Groups available in PDF, EPUB and Kindle.
