How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange...

The “power of choice” has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of random tree growth. In our models each new node has k randomly chosen contacts, where k 1 is a constant. It then attaches to...

A dynamical model of capital exchange is introduced in which a specified amount of capital is exchanged between two individuals when they meet. The resulting time dependent wealth distributions are determined for a variety of exchange rules. For ``greedy'' exchange, an interaction between a rich...

Networks growing according to the rule that every new node has a probability pk of being attached to k preexisting nodes, have a universal phase diagram and exhibit power-law decays of the distribution of cluster sizes in the non-percolating phase. The percolation transition is continuous but of...

An intriguing connection between extreme value statistics and traveling fronts has been found recently in a number of diverse problems. In this short review we outline a few such problems and consider their various applications.

We study opinion dynamics models where agents evolve via repeated pairwise interactions. In the compromise model, agents with sufficiently close real-valued opinions average their opinions. A steady state is reached with a finite number of isolated, noninteracting opinion clusters...

We study statistical properties of a one-dimensional infinite system of interacting particles. Each particle moves with constant velocity towards its closest neighbor and particles coalesce upon collisions. We propose a mean-field theory that predicts a t−1 concentration decay, confirmed by...