# Attracting random walks

@article{Gaudio2019AttractingRW, title={Attracting random walks}, author={Julia Gaudio}, journal={arXiv: Probability}, year={2019} }

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with probability proportional to the exponent of the number of other particles at a vertex. From an applied standpoint, the model captures the rich get richer phenomenon. We show that the Markov chain exhibits a phase transition in mixing time, as the parameter…

## One Citation

### Investigations in applied probability and high-dimensional statistics

- Mathematics, Computer Science
- 2020

This thesis makes contributions to the areas of applied probability and high-dimensional statistics by introducing the Attracting Random Walks model, which is a Markov chain model on a graph, and studying isotonic regression, a coordinate-wise monotone function from data.

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