Related papers: Weak survival for branching random walks on graphs
A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as v varies. The problem can be analyzed using the properties of the Fisher-Kolmogorov-Petrovsky-Piscounov (F-KPP)…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…
The aim of this paper is the study of the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite dimensional generating function G and a maximum principle…
In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying…
Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…
The branching annihilating random walk is studied on a random graph whose sites have uniform number of neighbors (z). The Monte Carlo simulations in agreement with the generalized mean-field analysis indicate that the concentration decreses…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…
Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…