Related papers: On Random Walks with a General Moving Barrier
Recently, we provided a simple but accurate formula which closely approximates the first crossing distribution associated with random walks having correlated steps. The approximation is accurate for the wide range of barrier shapes of…
We provide a simple formula that accurately approximates the first crossing distribution of barriers having a wide variety of shapes, by random walks with a wide range of correlations between steps. Special cases of it are useful for…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution…
Analytical approaches to galaxy formation and reionization are based on the mathematical problem of random walks with barriers. The statistics of a single random walk can be used to calculate one-point distributions ranging from the mass…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
Insight into a number of interesting questions in cosmology can be obtained from the first crossing distributions of physically motivated barriers by random walks with correlated steps. We write the first crossing distribution as a formal…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
We study transport within a spatially heterogeneous one-dimensional quantum walk with a combination of hierarchical and random barriers. Recent renormalization group calculations for a spatially disordered quantum walk with a regular…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…