Fluctuation Properties of the TASEP with Periodic Initial Configuration

Borodin, Alexei; Ferrari, Patrik L.; Prähofer, Michael; Sasamoto, Tomohiro

doi:10.1007/s10955-007-9383-0

Cited by 260 publications

(469 citation statements)

References 35 publications

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“…These computations lead to the asymptotic results of [7][8][9][10][11]48] for one-dimensional growth models with more general types of initial conditions.…”

Section: Other Connectionsmentioning

confidence: 99%

Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

Borodin

Ferrari

2013

Commun. Math. Phys.

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224

548

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We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models.The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece.(2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order ln(t) for time t ≫ 1. (3) There is a map of the (2 + 1)-dimensional space-time to the upper half-plane H such that on space-like submanifolds the multipoint fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on H.

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“…These computations lead to the asymptotic results of [7][8][9][10][11]48] for one-dimensional growth models with more general types of initial conditions.…”

Section: Other Connectionsmentioning

confidence: 99%

Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

Borodin

Ferrari

2013

Commun. Math. Phys.

Self Cite

224

548

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“…The computation of the joint distribution of particle positions at a given time t can be obtained from Proposition 2.1 by adapting the method used in [4] for the TASEP. However, one of the main motivation for this work is to enlarge the spectrum of the situations which can be analyzed to what we call space-like paths.…”

Section: Space-like Pathsmentioning

confidence: 99%

“…Therefore, the rescaled process is given by 12) where n(u) and t(u) are defined in (2.9). The rescaled process X T has a limit for large T given in terms of the Airy 1 process, A 1 (see [4,5,11] and Section 2.4 for details on A 1 ).…”

Section: Flat Initial Conditionsmentioning

confidence: 99%

“…For the TASEP and PNG models, large time fluctuation results have already been obtained in the following cases: For the step initial condition the Airy 2 process has been shown to occur in the scaling limit for fixed time [14,15,18], and more recently for tagged particle [13]. For TASEP, the Airy 1 process occurs for flat initial conditions in continuous time [4] and in discrete time with sequential update [3] with generalization to the initial condition of one particle every d ≥ 2 sites 1 . Also, a transition between the Airy 2 and Airy 1 processes was obtained in [5].…”

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confidence: 96%

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Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP

Borodin

Ferrari

Sasamoto

2008

Commun. Math. Phys.

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152

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We consider a new interacting particle system on the onedimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way.We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any space-like path are described by the Airy 1 and Airy 2 processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.

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“…In one way, our model could be regarded as a continuum, syncronous-moves analog of the (discrete-space, asynchronous moves) TASEP which has been intensively studied [4] owing to its connections with other statistical physics models. The small literature on such analogs of TASEP (see [3] and citations therein) has focused on ergodic properties for processes on the doubly-infinite line.…”

Section: Remarks On the Model And Related Workmentioning

confidence: 99%

Waves in a Spatial Queue

Aldous¹

2017

Stochastic Systems

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Envisaging a physical queue of humans, we model a long queue by a continuous-space model in which, when a customer moves forward, they stop a random distance behind the previous customer, but do not move at all if their distance behind the previous customer is below a threshold. The latter assumption leads to "waves" of motion in which only some random number W of customers move. We prove that P(W > k) decreases as order k −1/2 ; in other words, for large k the k'th customer moves on average only once every order k 1/2 service times. A more refined analysis relies on a non-obvious asymptotic relation to the coalescing Brownian motion process; we give a careful outline of such an analysis without attending to all the technical details.

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Fluctuation Properties of the TASEP with Periodic Initial Configuration

Cited by 260 publications

References 35 publications

Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP

Waves in a Spatial Queue

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