Related papers: Local Behavior of Airy Processes
For general $\beta \geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \to \infty$. For each fixed time, this ensemble is…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We provide some equations for the Variance Gamma process due to the fact that we do not consider only the definition as a time-changed Brownian motion. This brings us to a new non-local equation, even true in the drifted case, involving…
Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension…
We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak coupling limit, a path-integral formulation allows to compute the effective diffusion coefficient in the cases of an active…
We study boundary traces of shift-invariant diffusions: two-dimensional diffusions in the upper half-plane $\mathbb{R} \times [0, \infty)$ (or in $\mathbb{R} \times [0, R)$) invariant under horizontal translations. We prove that the…
We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current…
In this paper we discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to $\infty $.…
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=T^x(.,1), where T^x is the unique action in the Airy line ensemble satisfying a growth condition depending on x.…
We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by…
Active Brownian particles (ABPs) are termed out to be a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by…
The Airy distribution (AD) describes the probability distribution of the area under a Brownian excursion. The AD is prominent in several areas of physics, mathematics and computer science. Here we use a dilute colloidal system to directly…
Active and diffusive motion in Brownian particles are regularly observed in fluidic environments, albeit at different time scales. Here, we experimentally study the dynamics of highly asymmetric microclusters trapped in air employing…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
Biological tissues are active materials whose non-equilibrium dynamics emerge from distinct cellular force-generating mechanisms. Using a two-dimensional active foam model, we compare the effects of traction forces and junctional tension…
Consider the restriction of the directed landscape $\mathcal L(x, s; y, t)$ to a set of the form $\{x_1, \dots, x_k\} \times \{s_0\} \times \mathbb R \times \{t_0\}$. We show that on any such set, the directed landscape is given by a last…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…