Random Walks and Electric Networks - 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 and Electric Networks write by Peter G. Doyle. This book was released on 1984-12-31. Random Walks and Electric Networks available in PDF, EPUB and Kindle. Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Random Walks and Electric Networks
Random Walks and Electric Networks - 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 and Electric Networks write by Peter G. Doyle. This book was released on 1984. Random Walks and Electric Networks available in PDF, EPUB and Kindle.
Random Walks and Diffusions on Graphs and Databases
Random Walks and Diffusions on Graphs and Databases - 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 and Diffusions on Graphs and Databases write by Philipp Blanchard. This book was released on 2011-05-26. Random Walks and Diffusions on Graphs and Databases available in PDF, EPUB and Kindle. Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Probability on Trees and Networks
Probability on Trees and Networks - 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 Probability on Trees and Networks write by Russell Lyons. This book was released on 2017-01-20. Probability on Trees and Networks available in PDF, EPUB and Kindle. Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
Planar Maps, Random Walks and Circle Packing
Planar Maps, Random Walks and Circle Packing - 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 Planar Maps, Random Walks and Circle Packing write by Asaf Nachmias. This book was released on 2019-10-04. Planar Maps, Random Walks and Circle Packing available in PDF, EPUB and Kindle. This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
