scholarly journals Zero-one-only process: A correlated random walk with a stochastic ratchet

2014 ◽  
Vol 28 (29) ◽  
pp. 1450201
Author(s):  
Seung Ki Baek ◽  
Hawoong Jeong ◽  
Seung-Woo Son ◽  
Beom Jun Kim
Keyword(s):  
Transport Phenomenon ◽  
Random Walk ◽  
Random Walks ◽  
Stochastic Processes ◽  
Function Method ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Persistent Random Walk ◽  
The One ◽  
Previous Step

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability p, and stops to change the direction with 1 − p. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

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.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (1) ◽  
pp. 201-207
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (01) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (1) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (1) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Random walks and related diffusion equations

2004 ◽  
Vol 82 (11) ◽  
pp. 891-904
Author(s):  
P Moretti ◽  
M Lantieri ◽  
L Cianchi
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Random Walks ◽  
Physical Application ◽  
Diffusion Equations ◽  
One Dimensional ◽  
Discrete States ◽  
Points Of View ◽  
The One

The one-dimensional random walk between two reflecting walls is considered from two different points of view: the first, as a particular case of jumps between neighbouring, discrete states; the second, as a system that obeys a generalized diffusion equation. By performing the suitable limits, the identity of the two results is pointed out and a physical application is presented. PACS Nos.: 02.50.Ey, 02.30.Jr

scholarly journals Non-Gaussian fluctuations of randomly trapped random walks

2021 ◽  
Vol 53 (3) ◽  
pp. 801-838
Author(s):  
Adam Bowditch
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Sufficient Conditions ◽  
Infinite Variance ◽  
Correct Order ◽  
Main Motivation ◽  
One Dimensional ◽  
Stable Lévy Process ◽  
The One ◽  
Non Gaussian

AbstractIn this paper we consider the one-dimensional, biased, randomly trapped random walk with infinite-variance trapping times. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton–Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime.

scholarly journals Deterministic Random Walks on the Integers

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Joshua Cooper ◽  
Benjamin Doerr ◽  
Joel Spencer ◽  
Gábor Tardos
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Deterministic Process ◽  
One Dimensional ◽  
Space And Time ◽  
Dimensional Version ◽  
International Audience ◽  
The One

International audience We analyze the one-dimensional version of Jim Propp's $P$-machine, a simple deterministic process that simulates a random walk on $\mathbb{Z}$. The "output'' of the machine is astonishingly close to the expected behavior of a random walk, even on long intervals of space and time.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (01) ◽  
pp. 201-207 ◽  
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

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