We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

From the Publisher:
Although it originated as a method to study general dynamical systems, symbolic dynamics is useful in coding for data storage and transmission as well as in linear algebra. Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises.

An Introduction to Symbolic Dynamics and Coding

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

thomas m liggett. stochastic interacting systems contact voter and. new approach of financial volatility duration dynamics by. stochastic interacting systems contact voter and. stochastic interacting systems contact voter and core. exclusion processes springerlink. interacting particle systems thomas m liggett google. non homogeneous random walks by mikhail menshikov. coexistence in stochastic spatial models. thomas m liggett librarything. voter interacting systems applied to chinese stock markets. pdf download interacting full books pdfbooks. aldous interacting particle systems as stochastic social. macroscopic transport equations in many body systems from. liggett stochastic models of interacting systems. interacting particle system. voter interacting systems applied to chinese stock markets. stochastic interacting systems contact voter and. passage time moments and hybrid zones for the exclusion. stochastic interacting systems contact voter and. stochastic models for large interacting systems and. interacting particle systems thomas m liggett springer. interacting particle systems as stochastic social dynamics. citeseerx interacting particle systems as stochastic. interacting particle systems as stochastic social dynamics. stochastic models for large interacting systems in the. voter model. customer reviews stochastic interacting. additions and corrections for stochastic interacting. stochastic interacting systems contact voter. stochastic interacting systems contact voter and. entropy free full text entropy and recurrence mdpi. random walks in a queueing network environment journal. empirical analysis and agent based modeling of the. stochastic models for large interacting systems and. the noisy voter exclusion process request pdf. contact process mathematics. plex similarity and fluctuation dynamics of financial. spatial moran models i stochastic tunneling in the. stochastic models for large interacting systems and. stochastic interacting systems contact voter and. nonlinear stochastic interacting dynamics and plexity. stochastic interacting systems contact voter and. mathematical definition db0nus869y26v cloudfront net. stochastic interacting systems contact voter and. stochastic interacting systems contact voter and. stochastic domination for the last passage percolation model. table of contents for stochastic interacting systems. interacting particle systems as stochastic social dynamics. interacting particle systems thomas milton liggett

Stochastic Interacting Systems: Contact, Voter and Exclusion Processes

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

Shape Fluctuations and Random Matrices

Percolation and the hard-core lattice gas model

It is known that in one dimension an irreducible subshift of finite type has a unique measure of maximal entropy, the so-called Parry measure. Here we give a counterexample to this in higher dimensions. For this example, we also describe the geometric structure of the measures of maximal entropy and show that there are exactly two extremal measures.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0143385700007859

Non-uniqueness of measures of maximal entropy for subshifts of finite type

In this paper we studynon-interactive correlation distillation (NICD), a generalization of noise sensitivity previously considered in [5, 31, 39]. We extend the model toNICD on trees. In this model there is a fixed undirected tree with players at some of the nodes. One node is given a uniformly random string and this string is distributed throughout the network, with the edges of the tree acting as independent binary symmetric channels. The goal of the players is to agree on a shared random bit without communicating.

https://www.cims.nyu.edu/~regev/papers/beckner.pdf

Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality

One goal of this paper is to prove that dynamical critical site percolation on the planar triangular lattice has exceptional times at which percolation occurs. In doing so, new quantitative noise sensitivity results for percolation are obtained. The latter is based on a novel method for controlling the "level k" Fourier coefficients via the construction of a randomized algorithm which looks at random bits, outputs the value of a particular function but looks at any fixed input bit with low probability. We also obtain upper and lower bounds on the Hausdorff dimension of the set of percolating times. We then study the problem of exceptional times for certain "k-arm" events on wedges and cones. As a corollary of this analysis, we prove, among other things, that there are no times at which there are two infinite "white" clusters, obtain an upper bound on the Hausdorff dimension of the set of times at which there are both an infinite white cluster and an infinite black cluster and prove that for dynamical critical bond percolation on the square grid there are no exceptional times at which three disjoint infinite clusters are present.

/pdf/quantitative-noise-sensitivity-and-exceptional-times-for-1aawpomer5.pdf

Jeffrey E. Steif

Papers

Percolation and the hard-core lattice gas model

Non-uniqueness of measures of maximal entropy for subshifts of finite type

Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality

Quantitative noise sensitivity and exceptional times for percolation

Quantitative noise sensitivity and exceptional times for percolation