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Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particularExpand
The Bethe lattice spin glass revisited
Abstract:So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties,Expand
Analytic and Algorithmic Solution of Random Satisfiability Problems
A class of optimization algorithms that can deal with the proliferation of metastable states are introduced; one such algorithm has been tested successfully on the largest existing benchmark of K-satisfiability. Expand
Statistical properties of stock order books: empirical results and models
Abstract We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The mostExpand
Survey propagation: an algorithm for satisfiability
A new type of message passing algorithm which allows to find efficiently a satisfiable assignment of the variables in the difficult region and is iterative and composed of two main parts. Expand
Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
This paper presents the probabilistic approach to reconstruction and discusses its optimality and robustness, and develops the asymptotic analysis of the corresponding phase diagrams with and without measurement noise. Expand
Wealth condensation in a simple model of economy
We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that theExpand
Information, Physics, and Computation
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, andExpand