Related papers: Oscillatory correlation of delayed random walks
Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous…
The elephant random walk is a history-dependent random walk. We study a class of interacting elephant random walks. Our model includes the exclusion process as a special case. By means of Monte Carlo simulations and mean-field arguments, we…
We model financial transactions as random walks on activity-driven temporal networks. By enforcing fund conservation, our framework analytically derives heavy-tailed distributions for the stationary balances and transaction sizes.…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
We present here a system with collection of random walks relaying a signal in one dimension in the presence of delays. We are interested in the time for a signal to travel from one end (start) to the other end (finish) of the lined group of…
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important and rich tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding…
Quadrupeds transition spontaneously to various gait patterns (e.g., walk, trot, pace, gallop) in response to the locomotion speed. The generation of these gait patterns has been the subject of debate for a long time. We propose a coupled…
Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice.…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective…
We study a continuous time random walk on the $d$-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one…