Random Walk
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Related Articles from SNS
Decomposition of Anomalous Diffusion in two-state random walks
Announce Type: replace-cross Abstract: Two-state stochastic models, where motion alternates between distinct dynamical modes, are widely observed in complex systems. Here we study the Two-State Random Walk (TSRW), which switches between a continuous-time random walk (CTRW) rest state and a standard L'evy walk (LW) motion state, each with power-law distributed sojourn times.
Decomposition of Anomalous Diffusion in two-state random walks
arXiv:2606.00149v1 Announce Type: cross Abstract: Two-state stochastic models, where motion alternates between distinct dynamical modes, are widely observed in complex systems. Here we study the Two-State Random Walk (TSRW), which switches between a continuous-time random walk (CTRW) rest state and a standard L'evy walk (LW) motion state, each with power-law distributed sojourn times. Using anomalous diffusion decomposition, we show that TSRWs exhibit a generic coexistence of Joseph...
Recovering link-weight structure in complex networks with weight-aware random walks
arXiv:2508.07489v1 Announce Type: cross Abstract: Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper systematically investigates how different random walk strategies - traditional unweighted, strength-based, and fully weight-aware - keeps edge weight information when generating node embeddings. Using network...
Convergence Rates of Continuous-Time Random Walks to Time-Fractional Diffusions with Unbounded Coefficients
arXiv:2605.31471v1 Announce Type: cross Abstract: We investigate uniform weak convergence rates for probabilistic numerical methods applied to backward time-fractional diffusion equations whose dynamics are driven by diffusions with possibly unbounded coefficients, such as the Geometric Brownian Motion. The fractional structure is represented through a random time-change by the inverse of a stable subordinator. To approximate the underlying fractional dynamics, we combine discrete Markov...
Beyond Direct Retweets: Multi-Step Pathways in Italian COVID-19 Twitter
arXiv:2605.30551v1 Announce Type: new Abstract: We study how retweet interactions in large-scale Twitter debates are organized beyond direct links alone. Focusing on Twitter debate in Italy during the first phase of the COVID-19 pandemic, we combine a validated community-reconstruction pipeline with a higher-order random-walk framework to examine how short multi-step pathways redistribute attention across discursive communities. Rather than reconstructing observed cascades of individual...
From Boundary Crossings to Global Connectivity: A Minimal Mechanism in Structured Agent-Based Landscapes
arXiv:2606.07344v1 Announce Type: new Abstract: This study investigates a minimal mechanism through which local mobility heterogeneity produces global reconfiguration in structured agent-based systems. Agents move in a multi-attractor landscape, where a small fraction exhibits higher-mobility exploratory dynamics while the remainder remain locally constrained. By comparing random-walk exploration, interface-sensitive dynamics, novelty-biased exploration, and a flat-landscape control, I...
Comparing sliding-mode, bang-bang and linear-quadratic-Gaussian for steering an atomic clock
arXiv:2605.20156v2 Announce Type: replace Abstract: Accurate timekeeping relies on feedback that continually steers a local clock toward a higher-grade reference. We evaluate first-order sliding-mode control (SMC) for steering an atomic clock and benchmark it against two standards: linear-quadratic-Gaussian (LQG) control and the bang-bang (BB). All three are tested in a common numerical framework using the standard two-state clock model driven by white and random-walk-frequency noise.
Universal Theory of Decaying Turbulence
Announce Type: replace-cross Abstract: We derive an exact solution of the loop equation for freely decaying incompressible turbulence in arbitrary spatial dimension $d>1$. Using the Mandelstam identity in the loop dynamics, we prove that the nonlinear advection term reduces to a pure derivative and drops out of the momentum-loop equation. As a result, the momentum-loop equation becomes purely diffusive, admitting an exact geometric solution as a random walk on a circle. Despite this distinct...
Predictive Statistics Shape Emergent World Representations of Grid Walkers
Announce Type: replace Abstract: Next-token predictors often appear to develop internal representations of the latent world and its rules. The probabilistic nature of these models suggests a deep connection between the structure of the world and the geometry of probability distributions. In order to understand this link more precisely, we use a minimal stochastic process as a controlled setting: constrained random walks on a two-dimensional lattice that must reach a fixed endpoint after a...
The Information Content of Quasar Variability Light Curves: How Well Can we Infer Stochastic Model Parameters?
arXiv:2606.01496v1 Announce Type: cross Abstract: Quasar variability, driven by multi-scale physical processing within a relativistic accretion disk, is commonly modelled with stochastic time series models. The simplest of these is the Damped Random Walk (DRW), also known as the Ornstein-Uhlenbeck (OU) process. Here, we demonstrate that, when fitting such a model to quasar light curve data, the mean of the light curve, $\mu$, should not be fixed (which is the typical approach), as this leads...