Limit Theorems for the One-Dimensional Random Walk with Random Resetting to the Maximum

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Van Hao Can ◽  
Thai Son Doan ◽  
Van Quyet Nguyen
Keyword(s):  
Random Walk ◽  
Limit Theorems ◽  
One Dimensional ◽  
The One

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.

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.

Phase transition in one-dimensional random walk with partially reflecting boundaries

1985 ◽  
Vol 17 (03) ◽  
pp. 594-606 ◽  
Author(s):  
Ora E. Percus
Keyword(s):  
Random Walk ◽  
Transition Probability ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Boundary Case ◽  
Reflecting Boundaries ◽  
The Mean ◽  
The One ◽  
The Relationship ◽  
Asymptotic Forms

We consider an asymmetric random walk, with one or two boundaries, on a one-dimensional lattice. At the boundaries, the walker is either absorbed (with probability 1–ρ) or reflects back to the system (with probability p). The probability distribution (Pn (m)) of being at position m after n steps is obtained, as well as the mean number of steps before absorption. In the one-boundary case, several qualitatively different asymptotic forms of P n(m) result, depending on the relationship between transition probability and the reflection probability.

Phase transition in one-dimensional random walk with partially reflecting boundaries

1985 ◽  
Vol 17 (3) ◽  
pp. 594-606 ◽  
Author(s):  
Ora E. Percus
Keyword(s):  
Random Walk ◽  
Transition Probability ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Boundary Case ◽  
Reflecting Boundaries ◽  
The Mean ◽  
The One ◽  
The Relationship ◽  
Asymptotic Forms

We consider an asymmetric random walk, with one or two boundaries, on a one-dimensional lattice. At the boundaries, the walker is either absorbed (with probability 1–ρ) or reflects back to the system (with probability p).The probability distribution (Pn(m)) of being at position m after n steps is obtained, as well as the mean number of steps before absorption. In the one-boundary case, several qualitatively different asymptotic forms of Pn(m) result, depending on the relationship between transition probability and the reflection probability.

A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b > 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 <m <a) under different conditions.

A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (01) ◽  
pp. 169-175
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b &gt; 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 &lt;m &lt;a) under different conditions.

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