Chip-firing and rotor-routing on directed graphs
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 …
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
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 …
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 …
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 …
Instead of distributing chips randomly, each vertex serves its neighbours in a fixed order. We …
Measure sweeping processes
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 …
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 …
Instead of moving to a random neighbor, the neighbors are served in a fixed order. We …
[HTML][HTML] Deterministic random walks on the integers
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 …
process that simulates a random walk on a graph. Instead of distributing chips to randomly …
Pattern formation in growing sandpiles
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 …
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
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 …
walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel …
The rotor–router model on regular trees
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 …
a deterministic growth model analogous to internal DLA. We show that the set of occupied …