Related papers: The frog model on non-amenable trees
A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…
Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
We consider the random walk in an \emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of $\Zbold$ and $\Zbold_2$ and define the…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
We present a minimal non-Hermitian model where a topologically nontrivial complex energy spectrum is induced by inter-particle interactions. Our model consists of a one-dimensional chain with a dynamical non-Hermitian gauge field with…
Many processes and models --in biological, physical, social, and other contexts-- produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological…
A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…
We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…