# Interacting Urns on a Finite Directed Graph.

@article{Kaur2019InteractingUO, title={Interacting Urns on a Finite Directed Graph.}, author={G. Kaur and N. Sahasrabudhe}, journal={arXiv: Probability}, year={2019} }

Consider a finite directed graph $G=(V, E)$ and place an urn with balls of two colours: white and black, at each node at time $t=0$. The urns evolve, in discrete time, depending upon a common replacement matrix $R$ and the underlying graph structure. At each time-step, urns reinforce their neighbours according to a fixed replacement matrix $R$. We study asymptotic properties of the fraction of balls of either colour and obtain limit theorems for general replacement matrices. In particular, we… Expand

#### One Citation

A Finite Memory Interacting Pólya Contagion Network and its Approximating Dynamical Systems

- Computer Science, Mathematics
- ArXiv
- 2020

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