Related papers: Schubert polynomials and the inhomogeneous TASEP o…

Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We…

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of non-equilibrium statistical physics, the totally…

In this paper we prove a new generic vanishing theorem for $X$ a complete homogeneous variety with respect to an action of a connected algebraic group. Let $A, B_0\subset X$ be locally closed affine subvarieties, and assume that $B_0$ is…

The $n$-species totally asymmetric zero range process ($n$-TAZRP) on one-dimensional periodic chain studied recently by the authors is a continuous time Markov process where arbitrary number of particles can occupy the same sites and hop to…

We derive bulk asymptotics of skew-orthogonal polynomials (sop) $\pi^{\bt}_{m}$, $\beta=1$, 4, defined w.r.t. the weight $\exp(-2NV(x))$, $V (x)=gx^4/4+tx^2/2$, $g>0$ and $t<0$. We assume that as $m,N \to\infty$ there exists an $\epsilon >…

In the recent paper [arXiv:1612.06893] P. B\"urgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by $\delta_{k,n}$ the average number of projective $k$-planes in…

We determine diameters of Markov chains describing one-dimensional N -particle models with an exclusion interaction, namely the Ssep (symmetric simple exclusion process) and one of its non-reversible liftings, the lifted Tasep (totally…

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution…

Totally Asymmetric Simple Exclusion Process (TASEP) on $\mathbb{Z}$ is one of the classical exactly solvable models in the KPZ universality class. We study the "slow bond" model, where TASEP on $\mathbb{Z}$ is imputed with a slow bond at…

Research in combinatorics has often explored the asymmetric simple exclusion process (ASEP). The ASEP, inspired by examples from statistical mechanics, involves particles of various species moving around a lattice. With the traditional ASEP…

We investigate two closely related setups. In the first one we consider a TASEP-style system of particles with specified initial and final configurations. The probability of each history of the system is assumed to be equal. We show that…

Let F be the complete flag variety over Spec(Z) with the tautological filtration 0 \subset E_1 \subset E_2 \subset ... \subset E_n=E of the trivial bundle E over F. The trivial hermitian metric on E(\C) induces metrics on the quotient line…

We define an algorithm on fermionic and bosonic twisted multiline queues that projects to the multispecies totally asymmetric simple exclusion process (TASEP) and the totally asymmetric zero range process (TAZRP) on a ring, respectively.…

We study the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir of unlimited capacity. We elucidate how the steady states are controlled by the interplay between the reservoir population that…

We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a uniform density $\rho_-=1$, Johansson…

We investigate a Markov chain defined by Thomas Lam, which generalizes the multi-type TASEP on a ring to any Weyl group. For groups of type C we define an analogue of the multiline queues of Ferrari and Martin (which compute the stationary…

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the…

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…

Given permutations $\pi \in S_n$ and $\sigma \in S_k$, let $N_\sigma(\pi)$ denote the number of occurrences of $\sigma$ in $\pi$. While pattern avoidance and the distribution of pattern occurrences in permutations have been extensively…

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present…