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.

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.

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.

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.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

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.

scholarly journals A MULTIDIMENSIONAL SUBDIFFUSION MODEL WITH CHEMOTAXIS

2019 ◽  
Vol 11 (2) ◽  
pp. 1
Author(s):  
Bambang Hendriya Guswanto
Keyword(s):  
Mathematical Model ◽  
Probability Measure ◽  
Random Walks ◽  
Unit Ball ◽  
Dimensional Case ◽  
One Dimensional ◽  
The One ◽  
The Mathematical Model

The mathematical model for subdiffusion process with chemotaxis proposed by Langlands and Henry [1] for the one-dimensional case is extended to the multi-dimensional case. The model is derived from random walks process using a probability measure on a n-multidimensional unit ball $S^{n-1}$.

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