Long time tail for spacially inhomogeneous random walks

2008 ◽  
pp. 162-162
Author(s):  
Herbert Spohn
Keyword(s):  
Random Walks ◽  
Long Time ◽  
Inhomogeneous Random Walks

scholarly journals A limit theorem for a splitting distribution of a quantum walk

2018 ◽  
Vol 16 (03) ◽  
pp. 1850023
Author(s):  
Takuya Machida
Keyword(s):  
Limit Theorem ◽  
Probability Distribution ◽  
Random Walks ◽  
Discrete Time ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Unitary Evolution ◽  
Time Quantum ◽  
Long Time

Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

scholarly journals Long time asymptotics of non-symmetric random walks on crystal lattices

2017 ◽  
Vol 272 (4) ◽  
pp. 1553-1624 ◽  
Author(s):  
Satoshi Ishiwata ◽  
Hiroshi Kawabi ◽  
Motoko Kotani
Keyword(s):  
Random Walks ◽  
Crystal Lattices ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics

RANDOM WALKS ON KEBAB LATTICES: LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

1995 ◽  
Vol 09 (10) ◽  
pp. 601-606 ◽  
Author(s):  
D. CASSI ◽  
S. REGINA
Keyword(s):  
Random Walks ◽  
Linear Chain ◽  
Mean Square Displacement ◽  
Analytical Techniques ◽  
Mean Square ◽  
Ordered Structure ◽  
Ordered Structures ◽  
Asymptotic Expressions ◽  
Long Time ◽  
The Mean

Kebab lattices are ordered lattices obtained matching an infinite two-dimensional lattice to each point of a linear chain. Discrete time random walks on these structures are studied by analytical techniques. The exact asymptotic expressions of the mean square displacement and of the RW Green functions show an unexpected logarithmic behavior that is the first example of such kind of law on an ordered structure. Moreover the probability of returning to the origin shows the fastest long time decay ever found for recursive random walks.

Minima of independent time-inhomogeneous random walks

2020 ◽  
Vol 23 (03) ◽  
pp. 2050021
Author(s):  
Wanting Hou ◽  
Wenming Hong
Keyword(s):  
Random Walks ◽  
Second Order ◽  
Inhomogeneous Random Walks

In this paper, we will consider the minima of an exponentially growing number of independent time-inhomogeneous random walks, where the first- and second-order limit behaviors for the minima have been obtained.

Long-time tails in continuous-time random walks

1990 ◽  
Vol 41 (10) ◽  
pp. 5702-5704 ◽  
Author(s):  
Horst Schnörer ◽  
Alexander Blumen
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Long Time Tails ◽  
Long Time ◽  
Continuous Time Random Walks

A new approach to the long-time behavior of self-avoiding random walks

1992 ◽  
Vol 217 (1) ◽  
pp. 142-169 ◽  
Author(s):  
Steven Golowich ◽  
John Z Imbrie
Keyword(s):  
Random Walks ◽  
Time Behavior ◽  
Long Time Behavior ◽  
New Approach ◽  
Long Time

Long-time properties of random walks with a single trap

1998 ◽  
Vol 58 (4) ◽  
pp. 4128-4133 ◽  
Author(s):  
Wolfgang Pfluegl ◽  
Robert J. Silbey
Keyword(s):  
Random Walks ◽  
Long Time
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