Related papers: Combinatorial mappings of exclusion processes
The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming…
Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a…
We propose and study a one-dimensional (1D) model consisting of two lanes with open boundaries. One of the lanes executes diffusive and the other lane driven unidirectional or asymmetric exclusion dynamics, which are mutually coupled…
In this paper, we study staircase tableaux, a combinatorial object introduced due to its connections with the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. Due to their interesting connections, staircase tableaux have…
We study a two-species PASEP, in which there are two types of particles, "heavy" and "light," hopping right and left on a one-dimensional lattice of $n$ cells with open boundaries. In this process, only the "heavy" particles can enter on…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
The asymmetric simple exclusion process (ASEP) is an important model from statistical physics describing particles that hop randomly from one site to the next along an ordered lattice of sites, but only if the next site is empty. ASEP has…
Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many non-equilibrium processes can be described by suitable subsets of the equilibrium…
The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of…
The paper examines the construction and analysis of a new class of mixed exponential statistical structures that combine the properties of stochastic models and linear positive operators. The relevance of the topic is driven by the growing…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
We investigate the structure of non-equilibrium steady states (NESS) for a class of exactly solvable models in the setting of a chain with left and right reservoirs. Inspired by recent results on the harmonic model, we focus on models in…
The asymmetric simple inclusion process (ASIP) --- a lattice-gas model for unidirectional transport with irreversible aggregation --- has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
Using the generalized normally ordered form of words in a locally-free group of $n$ generators, we show that in the limit $n\to\infty$, the partition function of weighted directed lattice animals on a semi-infinite strip coincides with the…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a…
We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical…
A new mechanism leading to a random version of Burgers' equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically stochastic, non-entropic weak solution…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…