scholarly journals An invariance principle for one-dimensional random walks among dynamical random conductances

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Marek Biskup
Keyword(s):  
Random Walks ◽  
Invariance Principle ◽  
One Dimensional ◽  
Random Conductances

scholarly journals Quenched invariance principle for random walks on dynamically averaging random conductances

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Stein Andreas Bethuelsen ◽  
Christian Hirsch ◽  
Christian Mönch
Keyword(s):  
Random Walks ◽  
Invariance Principle ◽  
Random Conductances

Computer Simulations for Some One-Dimensional Models of Random Walks in Fluctuating Random Environment

2005 ◽  
Vol 121 (3-4) ◽  
pp. 361-372 ◽  
Author(s):  
C. Boldrighini ◽  
G. Cosimi ◽  
S. Frigio ◽  
A. Pellegrinotti
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Random Environment ◽  
One Dimensional ◽  
Dimensional Models

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

scholarly journals One dimensional quantum walks with memory

2010 ◽  
Vol 10 (5&6) ◽  
pp. 509-524
Author(s):  
M. Mc Gettrick
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Walks ◽  
One Dimensional ◽  
With Memory ◽  
Previous Step

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of one previous step. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

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