Generalizations of TASEP in Discrete and Continuous Inhomogeneous Space
Abstract
We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed first or lastpassage percolation models, or RobinsonSchenstedKnuth type systems with random input. One of the novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams. For systems with special steplike initial data, we find explicit limit shapes, describe hydrodynamic evolution, and obtain asymptotic fluctuation results which put the systems into the KardarParisiZhang universality class. At a critical scaling around a traffic jam in the continuous space TASEP, we observe deformations of the TracyWidom distribution and the extended Airy kernel, revealing the finer structure of this novel type of phase transitions. A homogeneous version of a discrete space system we consider is a oneparameter deformation of the geometric lastpassage percolation, and we obtain extensions of the limit shape parabola and the corresponding asymptotic fluctuation results. The exact solvability and asymptotic behavior results are powered by a new nontrivial connection to Schur measures and processes.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 December 2019
 DOI:
 10.1007/s00220019034954
 arXiv:
 arXiv:1808.09855
 Bibcode:
 2019CMaPh.372..797K
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Combinatorics
 EPrint:
 68 pages