5 citations · 13 across the 22 of their papers we have counts for
27 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…
Divisible sandpiles via random walks in random scenery
Ahmed Bou-Rabee, Yuval Peres, Ecaterina Sava-Huss
We analyze an optimal stopping problem for random walk in random scenery on general graphs, and determine when it has a finite optimum. We use this to extend a theorem of Levine, 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…
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…
Gaussian fluctuations for the two urn model
Konrad Kolesko, Ecaterina Sava-Huss
We introduce a modification of the generalized Pólya urn model containing two urns and we study the number of balls of a given color , …
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…
Limit theorems for discrete multitype branching processes counted with a characteristic
Konrad Kolesko, Ecaterina Sava-Huss
For a discrete time multitype supercritical Galton-Watson process and corresponding genealogical tree , we associate a new discrete time proce…
An epidemic model in inhomogeneous environment
Daniela Bertacchi, Jürgen Kampf, Ecaterina Sava-Huss +1
The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types diff…
Boundary behaviour of -polyharmonic functions on regular trees
Ecaterina Sava-Huss, Wolfgang Woess
This paper studies the boundary behaviour of -polyharmonic functions for the simple random walk operator on a regular tree, where is complex and , the -spect…
From fractals in external DLA to internal DLA on fractals
Ecaterina Sava-Huss
We present an unified approach on the behavior of two random growth models (external DLA and internal DLA) on infinite graphs, the second one being an internal counterpart of the f…
A law of large numbers for the range of rotor walks on periodic trees
Wilfried Huss, Ecaterina Sava-Huss
The aim of the current work is to prove a law of large numbers for the range size of recurrent rotor walks with random initial configuration on a general class of trees, called per…
Range and speed of rotor walks on trees
Wilfried Huss, Ecaterina Sava-Huss
We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton-Watson trees. More precisely, we show that on the clas…
Divisible sandpile on Sierpinski gasket graphs
Wilfried Huss, Ecaterina Sava-Huss
The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres as a tool to study internal diffusion limited aggregation. In this work we investig…
Internal DLA on Sierpinski gasket graphs
Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss +1
Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph which describes the formation of a random set of vertices growing from the origin (some fi…
Interpolating between random walk and rotor walk
Wilfried Huss, Lionel Levine, Ecaterina Sava-Huss
We introduce a family of stochastic processes on the integers, depending on a parameter and interpolating between the deterministic rotor walk (p=0) and the simple ra…