## Large deviations for independent random walks

Publication
, Journal Article

Cox, JT; Durrett, R

Published in: Probability Theory and Related Fields

March 1, 1990

We consider a system of independent random walks on ℤ. Let ξn(x) be the number of particles at x at time n, and let Ln(x)=ξ0(x)+ ... +ξn(x) be the total occupation time of x by time n. In this paper we study the large deviations of Ln(0)-Ln(1). The behavior we find is much different from that of Ln(0). We investigate the limiting behavior when the initial configurations has asymptotic density 1 and when ξ0(x) are i.i.d Poisson mean 1, finding that the asymptotics are different in these two cases. © 1990 Springer-Verlag.

### Duke Scholars

## Published In

Probability Theory and Related Fields

## DOI

## EISSN

1432-2064

## ISSN

0178-8051

## Publication Date

March 1, 1990

## Volume

84

## Issue

1

## Start / End Page

67 / 82

## Related Subject Headings

- Statistics & Probability
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Cox, J. T., & Durrett, R. (1990). Large deviations for independent random walks.

*Probability Theory and Related Fields*,*84*(1), 67–82. https://doi.org/10.1007/BF01288559Cox, J. T., and R. Durrett. “Large deviations for independent random walks.”

*Probability Theory and Related Fields*84, no. 1 (March 1, 1990): 67–82. https://doi.org/10.1007/BF01288559.Cox JT, Durrett R. Large deviations for independent random walks. Probability Theory and Related Fields. 1990 Mar 1;84(1):67–82.

Cox, J. T., and R. Durrett. “Large deviations for independent random walks.”

*Probability Theory and Related Fields*, vol. 84, no. 1, Mar. 1990, pp. 67–82.*Scopus*, doi:10.1007/BF01288559.Cox JT, Durrett R. Large deviations for independent random walks. Probability Theory and Related Fields. 1990 Mar 1;84(1):67–82.

## Published In

Probability Theory and Related Fields

## DOI

## EISSN

1432-2064

## ISSN

0178-8051

## Publication Date

March 1, 1990

## Volume

84

## Issue

1

## Start / End Page

67 / 82

## Related Subject Headings

- Statistics & Probability
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics