### Abstract

We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

Original language | English (US) |
---|---|

Pages (from-to) | 1103-1111 |

Number of pages | 9 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 47 |

Issue number | 5 |

State | Published - Oct 1987 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*47*(5), 1103-1111.

**ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.** / Percus, Ora E.; Percus, Jerome.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 47, no. 5, pp. 1103-1111.

}

TY - JOUR

T1 - ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.

AU - Percus, Ora E.

AU - Percus, Jerome

PY - 1987/10

Y1 - 1987/10

N2 - We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

AB - We consider the prototypical case of a lattice that is homogeneous in the large but inhomogeneous in the small - a one-dimensional random walk with alternating homogeneous lattice fragments and appropriate boundary probabilities. The generating function for the probability distribution of being at position x after N steps is obtained. We also find various asymptotic forms and limiting distributions as a function of the step probability and the lattice fragments.

UR - http://www.scopus.com/inward/record.url?scp=0023429750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023429750&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023429750

VL - 47

SP - 1103

EP - 1111

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -