Related papers: Persistence in Random Walk in Composite Media
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…
We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random…
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…
We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics…
The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…
We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n has the order of square root of n. Moment or symmetry assumptions are not necessary. In removing…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…
This article rigorously analyzes the meeting time between pursuers and evaders performing random walks on digraphs. There exist several bounds on the expected meeting time between random walkers on graphs in the literature, however,…
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…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
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…
The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…