### Abstract

In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N-1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N × N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].

Original language | English |
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Article number | 006 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 14 |

DOIs | |

Publication status | Published - Jan 12 2018 |

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### Keywords

- Bethe ansatz
- Second class particles
- TASEP

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

**On the TASEP with second class particles.** / Lee, Eunghyun.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the TASEP with second class particles

AU - Lee, Eunghyun

PY - 2018/1/12

Y1 - 2018/1/12

N2 - In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N-1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N × N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].

AB - In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N-1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N × N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].

KW - Bethe ansatz

KW - Second class particles

KW - TASEP

UR - http://www.scopus.com/inward/record.url?scp=85042017655&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042017655&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2018.006

DO - 10.3842/SIGMA.2018.006

M3 - Article

AN - SCOPUS:85042017655

VL - 14

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 006

ER -