### Abstract

With respect to a class of long-range exclusion processes on (Formula presented.), with single particle transition rates of order (Formula presented.), starting under Bernoulli invariant measure (Formula presented.) with density (Formula presented.), we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on (Formula presented.), d and (Formula presented.) with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter (Formula presented.). However, in the asymmetric case, we study the asymptotics of the variances, which when (Formula presented.) and (Formula presented.) points to a curious dichotomy between long-range strength parameters (Formula presented.) and (Formula presented.). In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.

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

Journal | Probability Theory and Related Fields |

DOIs | |

State | Accepted/In press - Sep 5 2015 |

### Fingerprint

### Keywords

- Additive functional
- Exclusion
- Exponent
- KPZ class
- Long-range
- Occupation time
- Simple

### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Statistics, Probability and Uncertainty

### Cite this

*Probability Theory and Related Fields*. https://doi.org/10.1007/s00440-015-0661-5

**Occupation times of long-range exclusion and connections to KPZ class exponents.** / Bernardin, Cédric; Gonçalves, Patrícia; Sethuraman, Sunder.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Occupation times of long-range exclusion and connections to KPZ class exponents

AU - Bernardin, Cédric

AU - Gonçalves, Patrícia

AU - Sethuraman, Sunder

PY - 2015/9/5

Y1 - 2015/9/5

N2 - With respect to a class of long-range exclusion processes on (Formula presented.), with single particle transition rates of order (Formula presented.), starting under Bernoulli invariant measure (Formula presented.) with density (Formula presented.), we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on (Formula presented.), d and (Formula presented.) with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter (Formula presented.). However, in the asymmetric case, we study the asymptotics of the variances, which when (Formula presented.) and (Formula presented.) points to a curious dichotomy between long-range strength parameters (Formula presented.) and (Formula presented.). In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.

AB - With respect to a class of long-range exclusion processes on (Formula presented.), with single particle transition rates of order (Formula presented.), starting under Bernoulli invariant measure (Formula presented.) with density (Formula presented.), we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on (Formula presented.), d and (Formula presented.) with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter (Formula presented.). However, in the asymmetric case, we study the asymptotics of the variances, which when (Formula presented.) and (Formula presented.) points to a curious dichotomy between long-range strength parameters (Formula presented.) and (Formula presented.). In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.

KW - Additive functional

KW - Exclusion

KW - Exponent

KW - KPZ class

KW - Long-range

KW - Occupation time

KW - Simple

UR - http://www.scopus.com/inward/record.url?scp=84940827727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940827727&partnerID=8YFLogxK

U2 - 10.1007/s00440-015-0661-5

DO - 10.1007/s00440-015-0661-5

M3 - Article

AN - SCOPUS:84940827727

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

ER -