Article
Mathematics, Applied
Shahid Zaman, Asad Ullah
Summary: This paper investigates the random walks of octagonal cell network by using the Laplacian spectrum method. The mean first passage time (τ) and Kemeny's constant (Ω) between nodes are obtained. The mean first passage time (τ) is explicitly studied in terms of the eigenvalues of a Laplacian matrix, while Kemeny's constant (Ω) is introduced to measure node strength and determine the scaling of the random walks. An explicit expression of Kemeny's constant and mean first passage time for octagonal cell network is provided based on Laplacian eigenvalues and the correlation among roots of characteristic polynomial. Comparative studies are also performed for τ and Ω based on the achieved results. This work also delivers an inclusive approach for exploring random walks of networks, particularly biased random walks, which can help better understand and tackle practical problems such as search and routing on networks.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
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
Physics, Multidisciplinary
Shahid Zaman, Mehreen Mustafa, Asad Ullah, Muhammad Kamran Siddiqui
Summary: This study presents a new graph spectrum-based approach to compute the mean first-passage time (MFPT) and Kemeny's constant (KC) of random walks on a penta-chain network ('O). By using the decomposition theorem of the normalized Laplacian polynomial, the normalized Laplacian matrix for the penta-chain network ('O) is computed. Formulas for both MFPT and KC for 'O are derived by utilizing the roots and coefficients of the obtained matrices. Finally, the results of MFPT and KC are compared with the number of pentagons.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Xiaomin Wang, Jing Su, Fei Ma, Bing Yao
Summary: In this paper, we generated a scale-free network using a rectangle operation and studied its topological structures, as well as characteristic quantities related to the network. These characteristic quantities can be used to evaluate network properties and have significant applications in science and engineering.
FRONTIERS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Debraj Das, Luca Giuggioli
Summary: This paper investigates lattice random walks with resetting dynamics. By constructing a discrete renewal equation and deriving closed-form expressions, the authors provide a formalism for analyzing various quantities in resetting dynamics based on the reset-free propagator or Green's function. The formalism is applied to biased random walks in one-dimensional unbounded space, and the continuous limits yield results consistent with diffusion with resetting. The paper also explores the resetting dynamics of biased random walkers with periodic and reflecting boundaries, and observes non-monotonic behavior in the first-passage probability in periodic domains as the resetting probability varies. Additionally, the authors study the transmission dynamics of two lattice walkers with resetting in a one-dimensional domain bounded by periodic and reflecting boundaries, and find non-monotonic behavior in the probability of definite transmission as the resetting probabilities change.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Multidisciplinary Sciences
Jinseong Son, Dongheyon Shin, Chi-Ok Hwang
Summary: Due to the isomorphism between electrostatic and Brownian diffusion problems, the induced charge density on a conducting surface is isomorphic to the first-passage probability of diffusion. Diffusion algorithms like WOS and WOH have been developed based on this isomorphism. The WOH algorithm performs better than the WOS algorithm in simulations of charge density distribution on parallel planes and mutual capacitance of circular plates.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics
A. Carmona, M. J. Jimenez, A. Martin
Summary: In the field of random walks, the mean first passage time matrix and Kemeny's constant are important parameters for studying networks. This paper focuses on obtaining expressions for these parameters using generalized inverses of the combinatorial Laplacian. The authors analyze the structure and relations between any generalized inverse and the group inverse of the combinatorial Laplacian, and provide closed-formulas for the mean first passage matrix and Kemeny's constant based on the group inverse of the combinatorial Laplacian. Wheel networks are used as an example to illustrate the findings.
LINEAR & MULTILINEAR ALGEBRA
(2023)
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
Physics, Mathematical
Clement Cosco, Inbar Seroussi, Ofer Zeitouni
Summary: This study examines the directed polymer model for general graphs and random walks beyond Z(d), providing conditions for the presence or absence of weak disorder phases, L-2 regions, and very strong disorder based on graph and random walk properties. The study delves into (biased) random walks on various trees, including Galton-Watson trees, and offers a range of examples that demonstrate counterexamples to intuitive extensions of the Z(d)/SRW results.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mechanics
Ido Tishby, Ofer Biham, Eytan Katzav
Summary: This study presents analytical results for the distribution of first-passage times of random walks on random regular graphs. The first-passage trajectories can be classified into those following the shortest path and those not following the shortest path.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
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, 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, Fluids & Plasmas
Gennaro Tucci, Andrea Gambassi, Satya N. Majumdar, Gregory Schehr
Summary: This study investigates the statistical properties of a single run-and-tumble particle (RTP) reaching a fixed target, with or without resetting, in one spatial dimension. By analyzing the first-passage time distribution of a free RTP and introducing resetting, the research reveals interesting singular behaviors and rich phase diagrams in the (b, v) plane, providing important insights into the behavior of RTP under different conditions.
Article
Physics, Multidisciplinary
Zhaole Wu, Xin Wang, Wenyi Fang, Longzhao Liu, Shaoting Tang, Hongwei Zheng, Zhiming Zheng
Summary: The study introduces a novel community detection algorithm called FPPM, which incorporates complete structural information within the maximal step length using a new similarity measure. Numerical simulations show that FPPM outperforms several classic algorithms on synthetic benchmarks and real-world networks, especially those with weak community structures.
Article
Physics, Multidisciplinary
Jing Su, Mingjun Zhang, Bing Yao
Summary: This study proposes a generalized weighted Koch network to characterize the topology and random walk of a random network. By replacing the triangles in the traditional Koch network with a probability graph R-s and assigning weights, the range of several indicators that can characterize the topological properties of the generalized weighted Koch network is determined. In addition, the average trapping time (ATT) in the trapping problem of the generalized weighted Koch network is analyzed, revealing the linear, super-linear, and sub-linear relationships between ATT and the number of nodes in the network.
