Related papers: Hammersley's process with sources and sinks

We classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\pm s_0\in S$, the spherical projection of $S\backslash\{\pm s_0\}$ to the hyperplane orthogonal to $\pm s_0$ is isometric to…

This work considers the distribution of inertial particles in turbulence using the point-particle approximation. We demonstrate that the random point process formed by the positions of particles in space is a Poisson point process with…

In a generic random system, the coexistence of extended and localized states can be evidenced by the subextensive width of energy distribution of a physical initial state in, for example, the quantum quenches which involving the local…

We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…

This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain $\Phi$. The approximations give rise to a natural sequence of control variates for the ergodic average…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with…

There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on…

We consider a L\'evy process $Y(t)$ that is not permanently observed, but rather inspected at Poisson($\omega$) moments only, over an exponentially distributed time $T_\beta$ with parameter $\beta$. The focus lies on the analysis of the…

We consider the Hammersley interacting particle system starting from a shock initial profile with densities $\lambda,\rho\in\mathbb{R}$ ($\lambda > \rho$). The microscopic shock is taken as the position of a second-class particle initially…

We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional…

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…

Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic…

Various best-choice problems related to the planar homogeneous Poisson process in finite or semi-infinite rectangle are studied. The analysis is largely based on properties of the one-dimensional box-area process associated with the…

With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the Poisson point process representation of the…

In this paper, we develop two stochastic models where the variable under consideration follows Harris distribution. The mean and variance of the processes are derived and the processes are shown to be non-stationary. In the second model,…

We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all…

We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using…

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…

We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered…