Two speed TASEP

Abstract

We consider the TASEP on Z with two blocks of particles having different jump rates. We study the large time behavior of particles' positions. It depends both on the jump rates and the region we focus on, and we determine the complete process diagram. In particular, we discover a new transition process in the region where the influence of the random and deterministic parts of the initial condition interact. Slow particles may create a shock, where the particle density is discontinuous and the distribution of a particle's position is asymptotically singular. We determine the diffusion coefficient of the shock without using second class particles. We also analyze the case where particles are effectively blocked by a wall moving with speed equal to their intrinsic jump rate.

51 pages, 7 figures, LaTeX

References in corpus (9)

• Asymptotics in ASEP with Step Initial Condition
• Fluctuation properties of the TASEP with periodic initial configuration
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• A determinantal formula for the GOE Tracy-Widom distribution
• Nonintersecting Brownian excursions
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

Cited by in corpus (19)

• Airy processes and variational problems
• Limit process of stationary TASEP near the characteristic line
• Universality of slow decorrelation in KPZ growth
• From interacting particle systems to random matrices
• Current fluctuations for TASEP: A proof of the Prähofer--Spohn conjecture
• Limit processes for TASEP with shocks and rarefaction fans
• Anomalous shock fluctuations in TASEP and last passage percolation models
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• Non-intersecting squared Bessel paths: critical time and double scaling limit
• Crossover distributions at the edge of the rarefaction fan
• Determinantal structures in the O'Connell-Yor directed random polymer model
• Supremum of the Airy2 process minus a parabola on a half line
• Shock fluctuations in flat TASEP under critical scaling
• On the partial connection between random matrices and interacting particle systems
• Crossover between various initial conditions in KPZ growth: flat to stationary
• Finite GUE distribution with cut-off at a shock
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• TASEP fluctuations with soft-shock initial data
• Asymptotics for the ratio and the zeros of multiple Charlier polynomials