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Introduction to percolation theory
Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion inExpand
Scaling theory of percolation clusters
Abstract For beginners : This review tries to explain percolation through the cluster properties; it can also be used as an introduction to critical phenomena at other phase transitions for readersExpand
Gelation and critical phenomena
For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolationExpand
Agent-based Models of Financial Markets
This review deals with several microscopic (‘agent-based’) models of financial markets which have been studied by economists and physicists over the last decade: Kim–Markowitz, Levy–Levy–Solomon,Expand
Phase Transitions in Two-Dimensional Kauffman Cellular Automata
In the random Boolean networks suggested by Kauffman, each site is changed to random rules depending on neighbours of this site. One can define two kinds of models, the annealed for which the randomExpand
Analysing tax evasion dynamics via the Ising model
We develop a model of tax evasion based on the Ising model. We augment the model using an appropriate enforcement mechanism that may allow policy makers to curb tax evasion. With a certainExpand
Random Site Percolation in Three Dimensions
We simulate sytems up to 10 001 × 10 001 × 10 001 in three dimensions at the percolation threshold pc of 0.31160. We find that the fractal dimension is ≃2.53±0.02, the cluster size distributionExpand
Self-organized percolation model for stock market fluctuations
In the Cont–Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixingExpand
Marketing Percolation
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in theExpand