Built on

C.A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel , Comm. Math. Phys. 159
Original
1994
Earlier work this paper cites.
T. Sasamoto and M. Wadati, Exact results for one-dimensional totally asymmetric diffusion models , J. Phys. A: Math. Gen. 31
1998
Earlier work this paper cites.
K. Johansson, Discrete polynuclear growth and determinantal processes , Comm. Math. Phys. 242
2003
Earlier work this paper cites.
T. Sasamoto, Spatial correlations of the 1D KPZ surface on a flat substrate , J. Phys. A 38
2005
Earlier work this paper cites.
A. Borodin, P.L. Ferrari, M. Prähofer, and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration , J. Stat. Phys. 129
2007
Earlier work this paper cites.
T. Imamura and T. Sasamoto, Dynamical properties of a tagged particle in the totally asymmetric simple exclusion process with the step-type initial condition , J. Stat. Phys. 128
2007
Earlier work this paper cites.
A. Borodin and P.L. Ferrari, Large time asymptotics of growth models on space-like paths I: PushASEP , Electron. J. Probab. 13
2008
Earlier work this paper cites.

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2013
Cited alongside, same era.

Then

G. Barraquand, A phase transition for q q -TASEP with a few slower particles (2014), arXiv:1404.7409
Original
2014
Closest in time.
A. Borodin and I. Corwin, Discrete time q q -TASEPs , to appear in Int. Math. Res. Not. IMRN (2014), arXiv:1305.2972
Original
2014
Closest in time.
A. Borodin and I. Corwin, Macdonald processes , Probab. Theory Relat. Fields 158
2014
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A. Borodin, I. Corwin, and P.L. Ferrari, Free energy fluctuations for directed polymers in random media in 1 + 1 1+1 dimension , Comm. Pure Appl. Math. 67
2014
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A. Borodin, I. Corwin, L. Petrov, and T. Sasamoto, Spectral theory for the q-Boson particle system , to appear in Compositio Mathematicae (2014), arXiv:1308.3475
Original
2014

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2013

Tracy-Widom asymptotics for q-TASEP

Ferrari, Patrik L., Veto, Balint

Understand

We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle.

For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.

Built on

C.A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel , Comm. Math. Phys. 159
Original
1994
Earlier work this paper cites.
T. Sasamoto and M. Wadati, Exact results for one-dimensional totally asymmetric diffusion models , J. Phys. A: Math. Gen. 31
1998
Earlier work this paper cites.
K. Johansson, Discrete polynuclear growth and determinantal processes , Comm. Math. Phys. 242
2003
Earlier work this paper cites.
T. Sasamoto, Spatial correlations of the 1D KPZ surface on a flat substrate , J. Phys. A 38
2005
Earlier work this paper cites.
A. Borodin, P.L. Ferrari, M. Prähofer, and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration , J. Stat. Phys. 129
2007
Earlier work this paper cites.
T. Imamura and T. Sasamoto, Dynamical properties of a tagged particle in the totally asymmetric simple exclusion process with the step-type initial condition , J. Stat. Phys. 128
2007
Earlier work this paper cites.
A. Borodin and P.L. Ferrari, Large time asymptotics of growth models on space-like paths I: PushASEP , Electron. J. Probab. 13
2008
Earlier work this paper cites.

Similar

P.L. Ferrari, From interacting particle systems to random matrices , J. Stat. Mech. (2010), P10016
2010
Cited alongside, same era.
I. Corwin, P.L. Ferrari, and S. Péché, Universality of slow decorrelation in KPZ models , Ann. Inst. H. Poincaré Probab. Statist. 48
2012
Cited alongside, same era.
N. O’Connell, Directed polymers and the quantum Toda lattice , Ann. Probab. 40
2012
Cited alongside, same era.
H. Spohn, KPZ scaling theory and the semi-discrete directed polymer model , MSRI Proceedings (2012) arXiv:1201.0645
Original
2012
Cited alongside, same era.
I. Corwin and L. Petrov, The q q -PushASEP: A new integrable model for traffic in 1 + 1 1+1 dimension , (2013), arXiv:1305.2972
Original
2013
Cited alongside, same era.

Then

G. Barraquand, A phase transition for q q -TASEP with a few slower particles (2014), arXiv:1404.7409
Original
2014
Closest in time.
A. Borodin and I. Corwin, Discrete time q q -TASEPs , to appear in Int. Math. Res. Not. IMRN (2014), arXiv:1305.2972
Original
2014
Closest in time.
A. Borodin and I. Corwin, Macdonald processes , Probab. Theory Relat. Fields 158
2014
Closest in time.
A. Borodin, I. Corwin, and P.L. Ferrari, Free energy fluctuations for directed polymers in random media in 1 + 1 1+1 dimension , Comm. Pure Appl. Math. 67
2014
Closest in time.
A. Borodin, I. Corwin, L. Petrov, and T. Sasamoto, Spectral theory for the q-Boson particle system , to appear in Compositio Mathematicae (2014), arXiv:1308.3475
Original
2014

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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M. Korhonen and E. Lee, The transition probability and the probability for the left-most particle’s position of the q q -TAZRP (2013), arXiv:1308.4769

Original

2013

Cited alongside, same era.

Closest in time.

A. Borodin, I. Corwin, and T. Sasamoto, From duality to determinants for q q -TASEP and ASEP , to appear in Ann. Probab. (2014), arXiv:1207.5035

Original

2014

Closest in time.