Related papers: Phase Transitions for Elephant Random Walks with T…
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
This contribution presents experimental study of two-dimensional pedestrian flow with the aim to capture the pedestrian behaviour within the cluster formed in front of the bottleneck. Two experiments of passing through a room with one…
We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…
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…
This paper investigates the long-time behavior of double branching annihilating random walkers with nearest-neighbor dependent rates. The system consists of even number of particles which can execute nearest-neighbor random walk and they…
Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
A 3D copepod trajectory is recorded in the laboratory, using 2 digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.
We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. We derive exact results for the probability of visiting a given number of sites and develop a…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter delta. For recurrence/transience the critical threshold is |delta|=1, for ballisticity it is |delta|=2 and for…
Quantifying space exploration is a central question in random walk theory, with direct applications ranging from animal foraging, diffusion-limited reactions, and intracellular transport to stock markets. In particular, the explored domain…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…