Statistics of TASEP with Three Merging Characteristics

Ferrari, Patrik L.; Nejjar, Peter

doi:10.1007/s10955-019-02447-5

Cited by 8 publications

(5 citation statements)

References 30 publications

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“…Remark 3.9. A similar result but for a different observable has been obtained with different methods in [22]. In that work, one analyzes the fluctuations of tagged particles in the case where two shocks with GOE Tracy-Widom distributed fluctuations merge.…”

Section: Two Colliding Gue-gue Shockssupporting

confidence: 56%

Shock fluctuations in TASEP under a variety of time scalings

Bufetov¹,

Ferrari²

2020

Preprint

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We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive an exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.

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Section: Two Colliding Gue-gue Shockssupporting

confidence: 56%

Shock fluctuations in TASEP under a variety of time scalings

Bufetov¹,

Ferrari²

2020

Preprint

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“…The comparison of TASEPs requires careful estimates, which will be done using the formalism of backwards paths discussed below. Backwards paths have been introduced in [Fer18], see also [FN20].…”

Section: Tightness Of the Scaled Particle Processmentioning

confidence: 99%

“…One interesting feature was a fluctuation description of a shock. Shocks were investigated on a deeper level in subsequent works by FN17,Nej18,Fer18,Nej19,FN20] and Quastel-Rahman [QR18]. Other types of evolution of the first particle were considered (and other initial condition on Z ≥0 as well), with fluctuations of different order and different distributions.…”

Section: Introductionmentioning

confidence: 99%

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TASEP with a moving wall

Borodin¹,

Bufetov²,

Ferrari³

2021

Preprint

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We consider a totally asymmetric simple exclusion on Z with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce asymptotic fluctuation distributions of particle positions of the formwith arbitrary barrier functions g. This is the same class of distributions that arises as one-point asymptotic fluctuations of TASEPs with arbitrary initial conditions. Examples include Tracy-Widom GOE and GUE distributions, as well as a crossover between them, all arising from various particles behind a linearly moving wall.We also prove that if the right-most particle is second class, and a linearly moving wall is shock-inducing, then the asymptotic distribution of the position of the second class particle is a mixture of the uniform distribution on a segment and the atomic measure at its right end.

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“…1 Such results hold around smooth limit shapes; hydrodynamical shocks can behave differently and we refer the reader to [33,40,[42][43][44][45]81] for some works on shocks. 2 The random initial condition on the two sides is recovered for most of the studied models using boundary sources, by the use of some Burke-type property [34,38], as shown for the exclusion process in [85].…”

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confidence: 90%

The half-space Airy stat process

Betea¹,

Ferrari

Occelli

2020

Preprint

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We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Péché, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.

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Statistics of TASEP with Three Merging Characteristics

Cited by 8 publications

References 30 publications

Shock fluctuations in TASEP under a variety of time scalings

Shock fluctuations in TASEP under a variety of time scalings

TASEP with a moving wall

The half-space Airy stat process

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