Related papers: Directed Continuous-Time Random Walk with memory
Vertex-Reinforced Random Walk (VRRW), defined by Pemantle (1988a), is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on…
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a…
We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim…
The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multi-dimensional generalization in which…
In this paper, we consider a spectral analysis of the Correlated Random Walk (CRW) on the path. We apply an analytical method for the Quantum Walk to CRW. For the isospectral coin cases, we obtain all of the eigenvalues and the…
Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…
It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since…
Since its introduction, some sixty years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad…
Self-driving vehicles plan around both static and dynamic objects, applying predictive models of behavior to estimate future locations of the objects in the environment. However, future behavior is inherently uncertain, and models of motion…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
In recent years a huge interdisciplinary field has emerged which is devoted to the complex dynamics of anomalous transport with long-time memory and non-markovian features. It was found that the framework of fractional calculus and its…
Annual maximum temperature data provides crucial insights into the impacts of climate change, especially for regions like India, where temperature variations have significant implications for agriculture, health, and infrastructure. In this…
Financial time series have historically been assumed to be a martingale process under the Random Walk hypothesis. Instead of making investment decisions using the raw prices alone, various multimodal pattern matching algorithms have been…
Research in human action recognition has accelerated significantly since the introduction of powerful machine learning tools such as Convolutional Neural Networks (CNNs). However, effective and efficient methods for incorporation of…
The study of quasar light curves poses two problems: inference of the power spectrum and interpolation of an irregularly sampled time series. A baseline approach to these tasks is to interpolate a time series with a Damped Random Walk (DRW)…
It is shown in this paper that the quantum master equation can be mapped to a modified continuous time random walk (CTRW) if the relaxation term is composed of transitions over a set of states. When the Hamiltonian is time-independent and…
We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting…
The continuous time random walk (CTRW) approach has been widely applied to model large-scale non-Fickian transport in the flow through disordered media. Often, the underlying microscopic transport mechanisms and disorder characteristics are…