# Bibliography

Journal Article

### A simple rank-based Markov chain with self-organized criticality

**: **Markov Processes and Related Fields vol.23, 1 (2017), p. 87-102

**: **GAP201/12/2613, GA ČR,
GA15-08819S, GA ČR

**: **self-reinforcement,
self-organized criticality,
canyon

**: **http://library.utia.cas.cz/separaty/2017/SI/swart-0476009.pdf

**(eng): **We introduce a self-reinforced point processes on the unit interval that appears to exhibit self-organized criticality, somewhat reminiscent of the well-known Bak-Sneppen model. The process takes values in the finite subsets of the unit interval and evolves according to the following rules. In each time step, a particle is added at a uniformly chosen position, independent of the particles that are already present. If there are any particles to the left of the newly arrived particle, then the left-most of these is removed. We show that all particles arriving to the left of p_c = 1 - e^{-1} are a.s. eventually removed, while for large enough time, particles arriving to the right of p_c stay in the system forever.

**: **BA

**: **10101