Related papers: Weak survival for branching random walks on graphs

Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…

It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…

We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.

Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr et.al. Each particle performs simple random walk…

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…

We demonstrate that continuous time quantum walks on several types of branching graphs, including graphs with loops, are identical to quantum walks on simpler linear chain graphs. We also show graph types for which such equivalence does not…

Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively…

We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary…

The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical…

We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength b_c exists such that most walks find the target within a finite time when b>b_c. For b<b_c,…

We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population…

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…

In a model of self-organized criticality unstable sites discharge to just one of their neighbors. For constant discharge ratio $\alpha$ and for a certain range of values of the input energy, avalanches are simple branchless P\'olya random…

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…

Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of $3$-cycles at least 2 and no cycles of lengths $5, 6, 7$…