相关论文: A Class of Multi-particle Reinforced Interacting R…
Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
We consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice. We assume that once walks meet, they coalesce. In $2d$, we classify the collective behavior of these walks under mild…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…
We revisit an unpublished paper of Vervoort (2002) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form $\mathbb{Z}\times \Gamma$, with $\Gamma$ a finite graph, for sufficiently large…
Over the last few years, network science has proved to be useful in modeling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
Random walks by single-node agents have been systematically conducted on various types of complex networks in order to investigate how their topologies can affect the dynamics of the agents. However, by fitting any network node, these…
Consider a finite undirected graph and place an urn with balls of two colours at each vertex. At every discrete time step, for each urn, a fixed number of balls are drawn from that same urn with probability $p$, and from a randomly chosen…
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…
Activated Random Walks, on $\mathbb{Z}^d$ for any $d\geqslant 1$, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen…
We present a theoretical analysis of a recent whole body motion planning method, the Randomized Possibility Graph, which uses a high-level decomposition of the feasibility constraint manifold in order to rapidly find routes that may lead to…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…