Transfer matrices for the totally asymmetric simple exclusion process

Totally asymmetric simple exclusion process

Unlike equilibrium statistical mechanics non-equilibrium statistical mechanics (NESM) has no wellestablished framework. The totally asymmetric simple exclusion process (TASEP) is one of the few models available that try to meet the challenge of describing NESM. Here TASEP is presented in its simplest version. Further two biological applications on mRNA translation and molecular motors are prese...

Totally asymmetric simple exclusion process on networks.

We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices c...

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

The time-integrated current of the TASEP has non-Gaussian fluctuations of order t. The recently discovered connection to random matrices and the Painlevé II RiemannHilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary two-point function. Some open problems ar...

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

Totally Asymmetric Exclusion Process

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz. From the properties of the algebra generated by the local jump operators, we construct explicitly the hierarchy of operators that commute with the Markov operator. The transfer matrix, which is the generating function of these operators, is shown to represent a discrete Markov proce...