Chip-firing and rotor-routing on directed graphs

AE Holroyd, L Levine, K Mészáros, Y Peres… - In and out of …, 2008 - Springer
Chip-Firing and Rotor-Routing on Directed Graphs Page 1 Progress in Probability, Vol. 60,
331–364 ©c 2008 Birkhauser Verlag Basel/Switzerland Chip-Firing and Rotor-Routing on …

Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile

L Levine, Y Peres - Potential Analysis, 2009 - Springer
The rotor-router model is a deterministic analogue of random walk. It can be used to define a
deterministic growth model analogous to internal DLA. We prove that the asymptotic shape …

Rotor walks and Markov chains

AE Holroyd, J Propp - Algorithmic probability and combinatorics, 2010 - books.google.com
The rotor walk is a derandomized version of the random walk on a graph. On successive
visits to any given vertex, the walker is routed to each of the neighboring vertices in some …

Deterministic random walks on the two-dimensional grid

B Doerr, T Friedrich - Combinatorics, Probability and Computing, 2009 - cambridge.org
Jim Propp's rotor–router model is a deterministic analogue of a random walk on a graph.
Instead of distributing chips randomly, each vertex serves its neighbours in a fixed order. We …

Measure sweeping processes

S Di Marino, B Maury, F Santambrogio - 2015 - hal.science
We propose and analyze a natural extension of the Moreau sweeping process: given a
family of moving convex sets (C (t)) t, we look for the evolution of a probability density ρt …

The cover time of deterministic random walks

T Friedrich, T Sauerwald - International Computing and Combinatorics …, 2010 - Springer
The rotor router model is a popular deterministic analogue of a random walk on a graph.
Instead of moving to a random neighbor, the neighbors are served in a fixed order. We …

[HTML][HTML] Deterministic random walks on the integers

J Cooper, B Doerr, J Spencer, G Tardos - European Journal of …, 2007 - Elsevier
Jim Propp's P-machine, also known as the 'rotor router model', is a simple deterministic
process that simulates a random walk on a graph. Instead of distributing chips to randomly …

Pattern formation in growing sandpiles

D Dhar, T Sadhu, S Chandra - Europhysics Letters, 2009 - iopscience.iop.org
Adding grains at a single site on a flat substrate in the Abelian sandpile models produces
beautiful complex patterns. We study in detail the pattern produced by adding grains on a …

[HTML][HTML] Bounds on the cover time of parallel rotor walks

D Dereniowski, A Kosowski, D Pająk… - Journal of Computer and …, 2016 - Elsevier
The rotor-router mechanism was introduced as a deterministic alternative to the random
walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel …

The rotor–router model on regular trees

I Landau, L Levine - Journal of Combinatorial Theory, Series A, 2009 - Elsevier
The rotor–router model is a deterministic analogue of random walk. It can be used to define
a deterministic growth model analogous to internal DLA. We show that the set of occupied …