scholarly journals Gaussian bounds and collisions of variable speed random walks on lattices with power law conductances

2016 ◽  
Vol 126 (10) ◽  
pp. 3041-3064
Author(s):  
Xinxing Chen
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Variable Speed ◽  
Gaussian Bounds

scholarly journals Clustered continuous-time random walks: diffusion and relaxation consequences

2012 ◽  
Vol 468 (2142) ◽  
pp. 1615-1628 ◽  
Author(s):  
Karina Weron ◽  
Aleksander Stanislavsky ◽  
Agnieszka Jurlewicz ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Continuous Time ◽  
Waiting Times ◽  
Scaling Limit ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
The Novel ◽  
Fractional Diffusion Equations ◽  
Continuous Time Random Walks

We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

2018 ◽  
Vol 20 (32) ◽  
pp. 20827-20848 ◽  
Author(s):  
Ru Hou ◽  
Andrey G. Cherstvy ◽  
Ralf Metzler ◽  
Takuma Akimoto
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Power Law ◽  
Waiting Time ◽  
Continuous Time ◽  
Zero Drift ◽  
Renewal Processes ◽  
Waiting Time Distributions ◽  
Continuous Time Random Walks ◽  
Ergodicity Breaking

We examine renewal processes with power-law waiting time distributions and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics.

scholarly journals Type Transition of Simple Random Walks on Randomly Directed Regular Lattices

2014 ◽  
Vol 51 (4) ◽  
pp. 1065-1080 ◽  
Author(s):  
Massimo Campanino ◽  
Dimitri Petritis
Keyword(s):  
Random Walk ◽  
Periodic Function ◽  
Random Walks ◽  
Power Law ◽  
Random Perturbation ◽  
Simple Random Walk ◽  
Critical Value ◽  
Absolute Value ◽  
Horizontal Orientation ◽  
Regular Lattices

Simple random walks on a partially directed version ofZ2are considered. More precisely, vertical edges between neighbouring vertices ofZ2can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function; the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.

scholarly journals Random Walks with Lookahead on Power Law Random Graphs

2006 ◽  
Vol 3 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Milena Mihail ◽  
Amin Saberi ◽  
Prasad Tetali
Keyword(s):  
Random Walks ◽  
Random Graphs ◽  
Power Law

Random walks with power-law fluctuations in the number of steps

2002 ◽  
Vol 35 (41) ◽  
pp. 8635-8645
Author(s):  
S V Annibaldi ◽  
K I Hopcraft
Keyword(s):  
Random Walks ◽  
Power Law

RANDOM WALKS, SELF-AVOIDING WALKS AND 1/f NOISE ON FINITE LATTICES

2004 ◽  
Vol 04 (03) ◽  
pp. L413-L424 ◽  
Author(s):  
FERDINAND GRÜNEIS
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Lattice Structure ◽  
Finite Lattice ◽  
The Self ◽  
Random Walker ◽  
Finite Lattices ◽  
Self Avoiding Walks

We investigate the probabilities for a return to the origin at step n of a random walker on a finite lattice. As a consistent measure only the first returns to the origin appear to be of relevance; these include paths with self-intersections and self-avoiding polygons. Their return probabilities are power-law distributed giving rise to 1/f b noise. Most striking is the behavior of the self-avoiding polygons exhibiting a slope b=0.83 for d=2 and b=0.93 for d=3 independent on lattice structure.

scholarly journals Invariance principle for variable speed random walks on trees

2017 ◽  
Vol 45 (2) ◽  
pp. 625-667 ◽  
Author(s):  
Siva Athreya ◽  
Wolfgang Löhr ◽  
Anita Winter
Keyword(s):  
Random Walks ◽  
Invariance Principle ◽  
Variable Speed
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