Related papers: A heterogeneous zero-range process related to a tw…
We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Dunkl processes are martingales as well as c\`{a}dl\`{a}g homogeneous Markov processes taking values in $\mathbb{R}^d$ and they are naturally associated with a root system. In this paper we study the jumps of these processes, we describe…
Many one-dimensional lattice particle models with open boundaries, like the paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not…
We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave…
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an…
We develop the connection between large deviation theory and more applied approaches to stochastic hybrid systems by highlighting a common underlying Hamiltonian structure. A stochastic hybrid system involves the coupling between a…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: The subset sum is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand…
The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads…
The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either $\pm\sigma$ is obtained. We find the electrostatic energy of…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…
Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with…
This paper presents a homogenisation-based constitutive model to describe the effective tran- sient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species…
In this paper we discuss a model describing global behavior of the two phase incompressible flow in fractured porous media. The fractured media is regarded as a porous medium consisting of two superimposed continua, a connected fracture…