For the inhomogeneous exponential corner growth model, the paper proves explicit variational formulas for the growth asymptotics, identifies the limit shape with flat segments and spikes, and derives the disordered TASEP flux and height functions.
Note on the flux for TASEP with general disorder
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abstract
Extending results of Bahadoran and Bodineau we show that the flux rate of TASEP with independent and identically distributed disorder always has a plateau of densities around $\frac12$.
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2019 1verdicts
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Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model
For the inhomogeneous exponential corner growth model, the paper proves explicit variational formulas for the growth asymptotics, identifies the limit shape with flat segments and spikes, and derives the disordered TASEP flux and height functions.