Related papers: Persistence exponents of self-interacting random w…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…
We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary.…
It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long-term memory. This is verified for the minimal extremally driven model, which is first defined and then solved…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
Extensive Monte Carlo simulations are performed in order to evaluate both the local ($\theta_{l}$) and global ($\theta_{g}$) persistence exponents in the Ziff-Gulari-Barshad (ZGB) (Phy. Rev. Lett. {\bf 56}, 2553, (1986)) irreversible…
We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…
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…
Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents…
We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…
We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the…