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Topics in Disordered Systems
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This chapter discusses ground States of Disordered Ferromagnets, which are states of highly Disordered Systems and Metastates found in high temperature systems and low temperature systems.Abstract:
0 Introduction.- 1 Ground States of Disordered Ferromagnets.- 2 Ground States of Highly Disordered Systems.- 3 High Temperature States of Disordered Systems.- 4 Low Temperature States of Disordered Systems.- Appendix A: Infinite Geodesice and Measurability.- Appendix B: Disordered Systems and Metastates.read more
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Probability on Trees and Networks
Russell Lyons,Yuval Peres +1 more
TL;DR: In this article, the authors present a state-of-the-art account of probability on networks, including percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks.
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The Random-Cluster Model
TL;DR: The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the theory of certain random combinatorial structures and of electrical networks as mentioned in this paper.
MonographDOI
Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction
Sacha Friedli,Yvan Velenik +1 more
TL;DR: In this paper, the authors give a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kac interactions.
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Iterative Methods for Toeplitz Systems
TL;DR: This chapter discusses Iterative methods, a method for solving the differential equations of toeplitz systems, and its applications to ordinary and partial differential equations.
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A First Course in Probability
TL;DR: In this paper, the authors propose a combinatorial approach for estimating the probability of a given self-test problem using a set of random variables, including continuous random variables and jointly distributed random variables.
Journal ArticleDOI
Bayesian Models for Multiple Local Sequence Alignment and Gibbs Sampling Strategies
TL;DR: This article develops a full Bayesian foundation for this Gibbs sampling algorithm and presents extensions that permit relaxation of two important restrictions and presents a rank test for the assessment of the significance of multiple sequence alignment.