Related papers: On the spatial persistence for Airy processes
We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply…
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…
The persistence behavior for fluctuating steps on the $Si(111)$ $(\sqrt3 \times \sqrt3)R30^{0} - Al$ surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970K. The measured persistence probability…
We study a spatial diffusion process generated by velocity fluctuations of intermittent nature. We note that intermittence reduces the entropy production rate while enhancing the diffusion strength. We study a case of space-dependent…
We show that the probability of a site being occupied at any instance of time in the one-dimensional randomly fluctuating hyperrectangles processes decreases monotonically with respect to its distance from the origin.
In this short note, we prove a refinement of bilinear local smoothing estimate to Airy solutions, when the frequency support of two wave are separated. As an application we prove a smoothing property of a bilinear form.
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear…
The maximal point of the Airy2 process minus a parabola is believed to describe the scaling limit of the end-point of the directed polymer in a random medium, which was proved to be true for a few specific cases. Recently two different…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…
The filamentational instability of spatially broadband femtosecond optical pulses in air is investigated by means of a kinetic wave equation for spatially incoherent photons. An explicit expression for the spatial amplification rate is…
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
The packing of hard-core particles in contact with their neighbors offers the statically determinate problem which allows analytical investigation of the stress tensor distribution. We construct the stress probability functional and derive…
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…
In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
We show the existence of superprocesses in a random medium with location dependent branching. Technically, we make use of a duality relation to establish the uniqueness of the martingale problem and to obtain the moment formulas.