Exact mean first-passage time on the T-graph

Abstract

We consider a simple random walk on the T-fractal and we calculate the exact mean time ${\tau }^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except $i_0$. By means of analytic techniques based on decimation procedures, we find the explicit expression for ${\tau }^g$ as a function of the generation $g$ and of the volume $V$ of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

6 pages

References in corpus (6)

• First-passage times in complex scale-invariant media
• Random walks on graphs: ideas, techniques and results
• Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration
• Ring structures and mean first passage time in networks
• Phase-ordering kinetics on graphs
• Autocatalytic reaction on low-dimensional substrates

Cited by in corpus (63)

• Random walks and diffusion on networks
• Geometry-controlled kinetics
• Global mean first-passage times of random walks on complex networks
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Random walks on weighted networks
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Characteristic times of biased random walks on complex networks
• Random Walks on deterministic Scale-Free networks: Exact results
• Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices
• Exact calculations of first-passage quantities on recursive networks
• Facilitated diffusion of proteins on chromatin
• Determining mean first-passage time on a class of treelike regular fractals
• Random walks in weighted networks with a perfect trap: An application of Laplacian spectra
• Mean first-passage time for random walks on undirected networks
• Mean first-passage time of surface-mediated diffusion in spherical domains
• Explicit determination of mean first-passage time for random walks on deterministic uniform recursive trees
• Random walks on the Apollonian network with a single trap
• Trapping in dendrimers and regular hyperbranched polymers
• Effective target arrangement in a deterministic scale-free graph
• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Trapping in scale-free networks with hierarchical organization of modularity
• Distinct scalings for mean first-passage time of random walks on scale-free networks with the same degree sequence
• Mean first-passage time for random walks on the T-graph
• Close or connected? Distance and connectivity effects on transport in networks
• Random walks in modular scale-free networks with multiple traps
• Exact calculations of first-passage properties on the pseudofractal scale-free web
• Mean first-passage time for maximal-entropy random walks in complex networks
• Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks
• Role of fractal dimension in random walks on scale-free networks
• Mean first-passage time for random walks in general graphs with a deep trap
• Impact of degree heterogeneity on the behavior of trapping in Koch networks
• Controlling the efficiency of trapping in treelike fractals
• Exact results for the first-passage properties in a class of fractal networks
• Complete spectrum of stochastic master equation for random walks on treelike fractals
• Efficiency analysis of diffusion on T-fractals in the sense of random walks
• Hitting and Trapping Times on Branched Structures
• Contact Kinetics in Fractal Macromolecules
• Analysis of diffusion and trapping efficiency for random walks on non-fractal scale-free trees
• Extended Vicsek fractals: Laplacian spectra and their applications
• Maximal entropy random walk improves efficiency of trapping in dendrimers
• Random walks in small-world exponential treelike networks
• Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps
• Local orientational mobility in regular hyperbranched polymers
• Mean trapping time for an arbitrary node on regular hyperbranched polymers
• Analysis of fluctuations in the first return times of random walks on regular branched networks
• First-passage properties of mortal random walks: ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs
• The normalized Laplacian spectrum of $n$-polygon graphs and its applications
• Dynamics of "comb-of-comb" networks
• Exact and Approximate Mean First Passage Times on Trees and other Necklace Structures: a Local Equilibrium Approach
• Random walks in unweighted and weighted modular scale-free networks with a perfect trap
• Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap
• Effects of node position on diffusion and trapping efficiency for random walks on fractal scale-free trees
• Anomalous behavior of trapping in extended dendrimers with a perfect trap
• Mean first-passage time of quantum transition processes
• Volatilities analysis of first-passage time and first-return time on a small-world scale-free network
• Scale-free tree network with an ultra-large diameter
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• A Method for Geodesic Distance on Subdivision of Trees with Arbitrary Orders and Their Applications
• Trapping problem on star-type graphs with applications
• Random walks on stochastic uniform growth trees: Analytical formula for mean first-passage time
• "Spectrally gapped" random walks on networks: a Mean First Passage Time formula
• Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases
• Exact mean first-passage time on generalized Vicsek fractal