The speed of the tagged particle in the exclusion process on Galton–Watson trees

Gantert, Nina; Schmid, Dominik

doi:10.1214/20-ejp477

Cited by 11 publications

(11 citation statements)

References 20 publications

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“…Proposition 1.2 (c.f. Proposition A.1 in [18]). Assume that for GW-almost every tree in T , the transition rates (r x,y ) are uniformly bounded from above.…”

Section: Tasep On Treesmentioning

confidence: 95%

“…Ideas to investigate the TASEP on trees can already be found in the physics literature as a natural way to describe transport on irregular structures, like blood, air or water circulations system; see [3,31,44]. Exclusion processes on trees, but with no forbidden directions, were studied when the particles perform symmetric simple random walks; see [9,18].…”

Section: Introductionmentioning

confidence: 99%

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The TASEP on Galton–Watson trees

Gantert

Georgiou

Schmid

2021

Electron. J. Probab.

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We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from x to y at rate rx,y provided y is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time t converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first n particles decouple.

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“…Proposition 1.2 (c.f. Proposition A.1 in [18]). Assume that for GW-almost every tree in T , the transition rates (r x,y ) are uniformly bounded from above.…”

Section: Tasep On Treesmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

The TASEP on Galton–Watson trees

Gantert

Georgiou

Schmid

2021

Electron. J. Probab.

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“…The behavior of the particle has also been investigated in other interacting particle processes, such as in zero range processes [10,13,27] and in stirring-exclusion processes [3]. Besides on the integer lattice Z d , the tagged particle was also considered on regular trees [2] and on Galton-Watson trees [5].…”

Section: Related Workmentioning

confidence: 99%

Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes

Xue,

Zhao

2022

Preprint

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We prove moderate deviation principles for the tagged particle position and current in one dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate 1/2, and the jump is suppressed if there is already one at the target site. We distinguish one particular particle which is called the tagged particle. We first establish a variational formula for the moderate deviation rate functions of the tagged particle positions based on moderate deviation principles from hydrodynamic limit proved by Gao and Quastel [6]. Then we construct a minimizer of the variational formula and obtain explicit expressions for the moderate deviation rate functions.

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“…Proposition 1.2 (c.f. Proposition A.1 in [17]). Assume that for GW-almost every tree in T , the transition rates (r x,y ) are uniformly bounded from above.…”

Section: Introductionmentioning

confidence: 95%

“…Ideas to investigate the TASEP on trees can already be found in the physics literature, see [3,30,43]. Exclusion processes on trees, but with no forbidden directions, were studied when the particles perform symmetric simple random walks, see [9,17]. In our setup, particles jump only in the direction pointing away from the root under the exclusion rule and choose their target site according to some jump kernel, that puts mass only on the children of their current location.…”

Section: Introductionmentioning

confidence: 99%