Random walk on Bethe lattice and hyperbolic geometry
arXiv:cond-mat/9509067 · doi:10.1088/0305-4470/29/10/019
Abstract
We give the exact solution to the problem of a random walk on the Bethe lattice through a mapping on an asymmetric random walk on the half-line. We also study the continuous limit of this model, and discuss in detail the relation between the random walk on the Bethe lattice and Brownian motion on a space of constant negative curvature.
12 pages. Revised version (minor changes) to appear in J. Phys. A
References in corpus (2)
Cited by in corpus (27)
- From Anderson localization on Random Regular Graphs to Many-Body localization
- Statistics of eigenstates near the localization transition on random regular graphs
- Analysis of self-organized criticality in Ehrenfest's dog-flea model
- Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
- Random walks and the Hagedorn transition
- On the relation between p-adic and ordinary strings
- Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization
- Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass
- Quantum oscillations in mesoscopic rings and anomalous diffusion
- Percolation Thresholds in Hyperbolic Lattices
- Diffusion on a heptagonal lattice
- Last-passage time for linear diffusions and application to the emptying time of a box
- Paths counting on simple graphs: from escape to localization
- Unraveling the structure of treelike networks from first-passage times of lazy random walkers
- Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane
- Random walk on disordered networks
- Codification Volume of an operator algebra and its irreversible growth through thermal processes
- Absence of Weak Localization on Negative Curvature Surfaces
- Random Walks on Intersecting Geometries
- On the asymptotic behavior of the hyperbolic Brownian motion
- Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
- Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
- Random walk with hyperbolic probabilities
- Path Counting on Tree-like Graphs with a Single Entropic Trap: Critical Behavior and Finite Size Effects
- Critical Dynamics of the Anderson Transition on Small-World Graphs
- Inferring Tree Structure with Hidden Traps from First Passage Times
- Displacement of transport processes on networked topologies