The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range processes for which a condensation transition arises. From urn models to zero-range processes: statics and dynamics 2 Introduction

Urn automata are a new class of automata consisting of an input tape, a finite-state controller, and an urn containing tokens with a finite set of colors, where the finite-state controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high prob...

1. Drawing balls without replacement (20 pts). Suppose that we have an urn containing one red ball and n − 1 white balls. Each time we draw a ball at random from the urn without replacement (so after the n-th drawing, there is no ball left in the urn). X i = 1 if the i-th ball is red, 0 otherwise.

The models surveyed include generalized Pólya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.

We test the hypothesis that superficial knowledge interdependence is more effective in fostering individual learning from collaboration than the true knowledge interdependence often realized by jigsaw-type collaboration arrangements. Based on research on group informationprocessing, we argue for the benefits of distributing only contextual information, but not core principles between learners, ...

Urn automata are a new class of automata consisting of an input tape, a finite-state controller, and an urn containing tokens with a finite set of colors, where the finite-state controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high prob...

Abstract. A general analytical treatment for the free energy of an urn model with quenched disorder is developed. It is revealed that the disordered urn model has similar mathematical structure to a random field Ising model. From this similarity, the free energy of the disordered urn model in the thermodynamic limit can be calculated from the canonical partition function by the replica analysis...

Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An contains coloured balls, which can be drawn probabilities proportional the numbers of balls each colour. For colour a tube is assumed. These tubes have different sizes (lengths). The idea that after drawing ball from it dropped corresponding We consider two associ...