Article
Physics, Multidisciplinary
J. Klinger, R. Voituriez, O. Benichou
Summary: We derive a universal and exact asymptotic form of the splitting probability for symmetric continuous jump processes, which highlights the importance of microscopic dynamics and provides explicit predictions for characterizing the effective random process in light scattering.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Fluids & Plasmas
Feng Huang, Hanshuang Chen
Summary: This study investigates discrete-time random walks with first-passage resetting processes on arbitrary networks, deriving exact expressions for stationary occupation probability, average number of resets, and mean first-passage time. Results show that these quantities can be expressed in terms of the fundamental matrix, demonstrating the advantage of first-passage resetting in global search on various networks.
Article
Physics, Multidisciplinary
Naftali R. Smith, Satya N. Majumdar, Gregory Schehr
Summary: This study investigates a random process x(tau) that undergoes stochastic resetting at a constant rate r with a position chosen from a distribution P(x). The study considers a sequence of dynamical observables A1, ..., An related to the intervals between resetting events. The study calculates the exact probabilities of various events associated with this sequence, such as the last element being larger than all previous ones, or the sequence being monotonically increasing. Remarkably, the study finds that these probabilities are super-universal, meaning they are independent of the specific process x(tau), the observables Ak's, and the resetting distribution P(x). The universality holds for some events as long as certain mild assumptions on the process and observables are met, such as mirror symmetry.
Article
Physics, Multidisciplinary
A. Barbier-Chebbah, O. Benichou, R. Voituriez
Summary: Self-interacting random walks with long-range memory effects have significant consequences on exploration properties. Attractive self-interactions provide advantages for local space exploration, while repulsive self-interactions accelerate global exploration.
Article
Physics, Multidisciplinary
William Graham Hoover, Carol Griswold Hoover, Edward Ronald Smith
Summary: Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zermelo's paradoxes. Studying the simplest model systems can enhance understanding of these paradoxical aspects of time-reversible systems.
Article
Physics, Multidisciplinary
Hanshuang Chen, Guofeng Li, Feng Huang
Summary: This paper investigates the effect of stochastic resetting on the first passage properties of discrete-time absorbing Markov chains. The authors derive the mean first passage time and splitting probabilities using a renewal approach. They also present a sufficient condition for optimizing the mean first passage time and apply their results to two specific examples.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Alejandro P. Riascos, Francisco Hernandez Padilla
Summary: In this paper, a framework for comparing differences in occupation probabilities of two random walk processes on networks is presented. The framework considers modifications of the network or the transition probabilities between nodes. A dissimilarity measure is defined using the eigenvalues and eigenvectors of the normalized Laplacian. The framework is used to examine differences in diffusive dynamics, the effect of new edges and rewiring in networks, and divergences in transport in degree-biased random walks and random walks with stochastic reset.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Applied
Emilio N. M. Cirillo, Matteo Colangeli, Antonio Di Francesco, Martin Kroger, Lamberto Rondoni
Summary: We investigate the deterministic dynamics of N point particles moving on a 2D table with two polygonal urns and an active rectangular channel. The study focuses on non-equilibrium phase transitions, ergodicity, and the dynamics of feedback-controlled biological systems.
Article
Physics, Fluids & Plasmas
Juan Ruben Gomez-Solano, Rosalio F. Rodriguez, Elizabeth Salinas-Rodriguez
Summary: In this work, we studied the dynamics of number-density fluctuations in a dilute suspension of active particles in a linear viscoelastic fluid. We proposed a model for the diffusion coefficient of the active particles that takes into account the rotational diffusion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, we derived the linearized equations for the active suspension and calculated its dynamic structure factor and intermediate scattering function. Our findings show that these functions exhibit complex dependencies on the parameters characterizing the viscoelasticity of the solvent and the activity of the particles, which differ significantly from those of inert suspensions and active suspensions in a Newtonian solvent. In certain regions of the parameter space, oscillations in the intermediate scattering function are observed, indicating the nonequilibrium particle activity and encoding the viscoelastic properties of the medium.
Article
Physics, Multidisciplinary
Yanik-Pascal Forster, Luca Gamberi, Evan Tzanis, Pierpaolo Vivo, Alessia Annibale
Summary: In this study, a novel method is proposed for calculating mean first-passage times (MFPTs) for random walks on graphs using dimensionality reduction technique. The method preserves the MFPTs between certain nodes and provides explicit formulae for MFPTs in specific graph structures. For other types of graphs, the generalized approximation method gives useful results.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Long Gao, Junhao Peng, Chunming Tang
Summary: The study focused on the first-passage process on fractal scale-free trees, examining the impact of the time to reach the target site on network transport efficiency. By introducing proper weights and the parameter w, the process was accelerated, and a method to find the minimum GMFPT was presented.
FRACTAL AND FRACTIONAL
(2021)
Article
Statistics & Probability
Amaury Freslon, Lucas Teyssier, Simeng Wang
Summary: In this paper, we consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time N ln(N). We then study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semicircle law. We also prove similar results for quantum permutations and quantum random transpositions.
PROBABILITY THEORY AND RELATED FIELDS
(2022)
Article
Physics, Multidisciplinary
M. Dahlenburg, G. Pagnini
Summary: We study the mean first-passage time (MFPT) for asymmetric continuous-time random walks characterized by waiting-times with finite mean and jump-sizes with finite mean and variance. We derive a nonhomogeneous Wiener-Hopf integral equation that allows for the exact calculation of the MFPT, which depends on the distribution of jump-sizes and the mean-value of waiting-times. Through a case study, we show that the MFPT is independent of the jump-sizes distribution in the opposite direction to the boundary and depends on the specific distribution of jump-sizes for starting points near the boundary.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Statistics & Probability
J. E. A. N. BERTOIN, H. A. I. R. U. O. YANG
Summary: The paper investigates the domains of attraction of branching-stable processes and provides explicit conditions for a branching random walk to converge to a branching-stable process after proper magnification. This presents a contrasting approach to the asymptotic behavior of branching random walks compared to previous studies.
JOURNAL OF APPLIED PROBABILITY
(2022)
Article
Physics, Multidisciplinary
Tomoshige Miyaguchi
Summary: The paper introduces a generalized Langevin equation with fluctuating diffusivity (GLEFD) and demonstrates that it satisfies a generalized fluctuation-dissipation relation. When the memory kernel follows a power law, the GLEFD displays subdiffusion, non-Gaussianity, and stretched-exponential relaxation. The case where the memory kernel is a single exponential function is also discussed, revealing plateau structures in the mean-square displacement and self-intermediate-scattering function of the system. Additionally, a numerical scheme for integrating the GLEFD is presented.
PHYSICAL REVIEW RESEARCH
(2022)