# Recent Publications

• Power series solution of the inhomogeneous exclusion process
arXiv:1803.00887

• Deciphering mRNA Sequence Determinants of Protein Production Rate
arXiv:1708.07678

• Conditioned random walks and interaction-driven condensation
J. Phys. A: Math. Theor. 50 024005 (2017)

# Recent Posts

### Paper submitted on the power series solution of the inhomogeneous TASEP

This is a follow-up to my previous paper on the inhomogeneous exclusion process done in collaboration with M. Carmen Romano (University of Aberdeen, UK) and Luca Cinadrini (Université de Montpellier, France). In this paper we study the standard totally asymmetric simple exclusion process (TASEP) with open boundary conditions and site-dependent hopping rates $\omega_i$ in the bulk, which is depicted below. We consider a steady-state probability $P(C)$ to find the system in a configuration $C$ and develop a power series of $P(C)$ in the entrance rate $\alpha$: $$P(C)=\sum_{n=0}^{\infty}c_n(C)\alpha^n$$ In particular, we show that $c_n(C)\neq 0$ if and only if $n\geq N(C)$, where $N(C)$ is the total number of particles in configuration $C$.

### Paper accepted in Physical Review Letters

My paper with Luca Cinadrini (Université de Montpellier, France) and M. Carmen Romano (University of Aberdeen, UK) has been accepted for publication in Physical Review Letters. We will soon submit a longer, more detailed paper to Physical Review E.

### Paper submitted on the rate of protein production

My new paper with Luca Cinadrini (Université de Montpellier, France) and M. Carmen Romano (University of Aberdeen, UK) addresses a long-standing problem in nonequilibrium statistical physics, namely finding the steady state of the totally asymmetric simple exclusion process (TASEP) with non-uniform hopping rates. The TASEP is a driven lattice gas of particles moving unidirectionally along a one-dimensional lattice of $L$ sites, whereby each site can hold at most one particle. Particles can enter the lattice at the rate $\alpha$ and leave at the rate $\beta$ (see the schematic figure below).