Related papers: From transience to recurrence with Poisson tree fr…
We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
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 the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
Even though the evolution of an isolated quantum system is unitary, the complexity of interacting many-body systems prevents the observation of recurrences of quantum states for all but the smallest systems. For large systems one can not…
We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
Inverse power law distributions are generally interpreted as a manifestation of complexity, and waiting time distributions with power index \mu < 2 reflect the occurrence of ergodicity breaking renewal events. In this Letter we show how to…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We consider a system of independent branching random walks on $\R$ which start off a Poisson point process with intensity of the form $e_{\lambda}(du)=e^{-\lambda u}du$, where $\lambda\in\R$ is chosen in such a way that the overall…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call…
In this paper, we consider the threshold-one contact process and the threshold-one voter model w/o spontaneous death on homogeneous trees $\mathbb{T}_d$, $d\ge 2$. Mainly inspired by the corresponding arguments for ordinary contact…
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…
The Tree Builder Random Walk is a special random walk that evolves on trees whose size increases with time, randomly and depending upon the walker. After every s steps of the walker, a random number of vertices are added to the tree and…
The notion of degree and related notions concerning recurrence and transience for a class of L'evy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is examined with emphasis on the role of the…
We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population…
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 demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…