### Abstract

We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (log t) for general rates, and at least t(log t) ^{1/2} for rates which are asymmetric only in the direction of one of the axes. These estimates give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

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

Pages (from-to) | 787-802 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 123 |

Issue number | 4 |

DOIs | |

State | Published - May 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Second-class particle
- Secondary 60F05
- Simple exclusion AMS (2000) subject classifications: Primary 60K35
- Variance of occupation times

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Superdiffusivity of occupation-time variance in 2-dimensional asymmetric exclusion processes with density ρ = 1/2.** / Sethuraman, Sunder.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Superdiffusivity of occupation-time variance in 2-dimensional asymmetric exclusion processes with density ρ = 1/2

AU - Sethuraman, Sunder

PY - 2006/5

Y1 - 2006/5

N2 - We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (log t) for general rates, and at least t(log t) 1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

AB - We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (log t) for general rates, and at least t(log t) 1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of "second-class" particles.

KW - Second-class particle

KW - Secondary 60F05

KW - Simple exclusion AMS (2000) subject classifications: Primary 60K35

KW - Variance of occupation times

UR - http://www.scopus.com/inward/record.url?scp=33747711339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747711339&partnerID=8YFLogxK

U2 - 10.1007/s10955-006-9061-7

DO - 10.1007/s10955-006-9061-7

M3 - Article

VL - 123

SP - 787

EP - 802

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 4

ER -