# ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS.

Ora E. Percus, Jerome Percus

Research output: Contribution to journalArticle

### 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) 1103-1111 9 SIAM Journal on Applied Mathematics 47 5 Published - Oct 1987

### Fingerprint

Random walk
Fragment
Probability distributions
Limiting Distribution
Generating Function
Probability Distribution
Form

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

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

In: SIAM Journal on Applied Mathematics, Vol. 47, No. 5, 10.1987, p. 1103-1111.

Research output: Contribution to journalArticle

Percus, Ora E. ; Percus, Jerome. / ONE-DIMENSIONAL RANDOM WALK IN ALTERNATING HOMOGENEOUS DOMAINS. In: SIAM Journal on Applied Mathematics. 1987 ; Vol. 47, No. 5. pp. 1103-1111.
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