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Probability on Graphs
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  • Cited by 32
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    KELLER, NATHAN 2011. On the Influences of Variables on Boolean Functions in Product Spaces. Combinatorics, Probability and Computing, Vol. 20, Issue. 01, p. 83.

    VAN ENTER, AERNOUT C. D. IACOBELLI, GIULIO and TAATI, SIAMAK 2012. POTTS MODEL WITH INVISIBLE COLORS: RANDOM-CLUSTER REPRESENTATION AND PIROGOV–SINAI ANALYSIS. Reviews in Mathematical Physics, Vol. 24, Issue. 02, p. 1250004.

    van den Berg, J. and Jonasson, J. 2012. A BK inequality for randomly drawn subsets of fixed size. Probability Theory and Related Fields, Vol. 154, Issue. 3-4, p. 835.

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    Ericson, Josh Poggi-Corradini, Pietro and Zhang, Hainan 2014. Effective resistance on graphs and the epidemic quasimetric. Involve, a Journal of Mathematics, Vol. 7, Issue. 1, p. 97.

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    Sin, Duho Kim, Jinsoo Choi, Jee Hyun and Kim, Sung-Phil 2014. Neuronal Ensemble Decoding Using a Dynamical Maximum Entropy Model. Journal of Applied Mathematics, Vol. 2014, Issue. , p. 1.

    Grimmett, Geoffrey R. and Manolescu, Ioan 2014. Bond percolation on isoradial graphs: criticality and universality. Probability Theory and Related Fields, Vol. 159, Issue. 1-2, p. 273.

    Kroese, Dirk P. Brereton, Tim Taimre, Thomas and Botev, Zdravko I. 2014. Why the Monte Carlo method is so important today. Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 6, Issue. 6, p. 386.

    Cruise, James R. Hryniv, Ostap O. and Wade, Andrew R. 2015. digital Encyclopedia of Applied Physics. p. 1.

    Leplaideur, Renaud 2015. Chaos: Butterflies also Generate Phase Transitions. Journal of Statistical Physics, Vol. 161, Issue. 1, p. 151.

    Correa, José Kiwi, Marcos Olver, Neil and Vera, Alberto 2015. Web and Internet Economics. Vol. 9470, Issue. , p. 272.

    Jorgensen, Palle and Tian, Feng 2015. Infinite networks and variation of conductance functions in discrete Laplacians. Journal of Mathematical Physics, Vol. 56, Issue. 4, p. 043506.

    Coletti, Cristian F. de Oliveira, Karina B. E. and Rodriguez, Pablo M. 2016. A stochastic two-stage innovation diffusion model on a lattice. Journal of Applied Probability, Vol. 53, Issue. 04, p. 1019.

    Weigel, Martin Elci, Eren Metin and Fytas, Nikolaos G. 2016. Connectivity properties of the random-cluster model. Journal of Physics: Conference Series, Vol. 681, Issue. , p. 012014.

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    Probability on Graphs
    • Online ISBN: 9780511762550
    • Book DOI: https://doi.org/10.1017/CBO9780511762550
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Book description

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm–Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Reviews

'The book under review serves admirably for this 'getting started' purpose. It provides a rigorous introduction to a broad range of topics centered on the percolation-IPS field discussed above … This book, like a typical Part III course, requires only undergraduate background knowledge but assumes a higher level of general mathematical sophistication. It also requires active engagement by the reader. As I often tell students, 'Mathematics is not a spectator sport - you learn by actually doing the exercises!' For the reader who is willing to engage the material and is not fazed by the fact that some proofs are only outlined or are omitted, this style enables the author to cover a lot of ground in 247 pages.'

David Aldous Source: Bulletin of the American Mathematical Society

'It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it. It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics.'

R.S. MacKay Source: Contemporary Physics

'This is clearly a successful advanced textbook.'

Fernando Q. Gouvêa Source: MAA Reviews

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