2 citations · 3 across the 16 of their papers we have counts for
16 papers
Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices
Robin Kaiser, Ecaterina Sava-Huss, Julia Überbacher
We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configu…
Phase transition for the asymptotic entropy of branching random walks on groups
Jeremie Brieussel, Robin Kaiser, Martin Klötzer +1
We consider supercritical branching random walks (BRW) on countable groups and we prove that the asymptotic entropy of the empirical distributions of the BRW has a phase transi…
Law of the Iterated Logarithm for -Walks on
Robin Kaiser
The -rotor walk on is a self-interacting walk that interpolates between the simple random walk and the deterministic rotor walk. While the weak convergence of this…
Limit shape of single-source stochastic sandpiles with -topplings on
David Beck-Tiefenbach, Robin Kaiser, Julia Überbacher
We investigate the limit shape of the single-source model for stochastic sandpiles on the integer line subject to --topplings. In this model, an initial configuration of $n\in\m…
Stabilization of stochastic networks in Markovian environment
Robin Kaiser, Martin Klötzer, Ecaterina Sava-Huss
We establish criteria under which stochastic networks in a Markovian environment stabilize, thus confirming Conjecture 7.2 from Levine-Greco [GL23]. The networks evolve on finite c…
Stochastic Sandpiles with Uniform Toppling Rule on the Line
David Beck-Tiefenbach, Robin Kaiser
We consider the stochastic sandpile model with uniform toppling rule on the integer line. During a uniform toppling, with probability one particle is sent to the right of the…
Maximal and minimal displacement of supercritical branching random walks on free products of groups
Robin Kaiser, Martin Klötzer, Konrad Kolesko +1
We prove that the maximal and minimal displacement of branching random walks with mean offspring number on free products of finite groups grows linearly almost surely. More p…
On the structure of the sandpile identity element on Sierpinski gasket graphs
Robin Kaiser, Ecaterina Sava-Huss, Julia Überbacher
We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converge…
Limit theorems for the empirical distribution of supercritical branching random walks on transitive graphs
Robin Kaiser, Martin Klötzer, Ecaterina Sava-Huss
We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type ce…
Locally Markov walks on finite graphs
Robin Kaiser, Lionel Levine, Ecaterina Sava-Huss
Locally Markov walks are natural generalizations of classical Markov chains, where instead of a particle moving independently of the past, it decides where to move next depending o…
Sandpiles on the Vicsek fractal explode with probability 1/4
Nico Heizmann, Robin Kaiser, Ecaterina Sava-Huss
Vicsek fractal graphs are an important class of infinite graphs with self similar properties, polynomial growth and treelike features, on which several dynamical processes such as…
Scaling limit of the sandpile identity element on the Sierpinski gasket
Robin Kaiser, Ecaterina Sava-Huss
We investigate the identity element of the sandpile group on finite approximations of the Sierpinski gasket with normal boundary conditions and show that the sequence of piecewise…
Average height for Abelian sandpiles and the looping constant on Sierpinski graphs
Nico Heizmann, Robin Kaiser, Ecaterina Sava-Huss
For the Abelian sandpile model on Sierpinski graphs, we investigate several statistics such as average height, height probabilities and looping constant. In particular, we calculat…
Internal aggregation models with multiple sources and obstacle problems on Sierpinski gaskets
Uta Freiberg, Nico Heizmann, Robin Kaiser +1
We consider the doubly infinite Sierpinski gasket graph , rescale it by factor , and on the rescaled graphs , for every , we investi…
Random rotor walks and i.i.d. sandpiles on Sierpinski graphs
Robin Kaiser, Ecaterina Sava-Huss
We prove that, on the infinite Sierpinski gasket graph SG, rotor walk with random initial configuration of rotors is recurrent. We also give a necessary condition for an i.i.d. san…
Abelian sandpiles on Sierpinski gasket graphs
Robin Kaiser, Ecaterina Sava-Huss, Yuwen Wang
The aim of the current work is to investigate structural properties of the sandpile group of a special class of self-similar graphs. More precisely, we consider Abelian sandpiles o…