Related papers: Noncolliding processes, matrix-valued processes an…
We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…
Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio=reactio on coarse-grained length and time scales.…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Recent progress in experimental techniques such as single particle tracking allows to analyze both nonequilibrium properties and approach to equilibrium. There are examples showing that processes occurring at finite timescales are…
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
This paper is a step in the direction of understanding the behavior of non-intersecting Brownian motions on the real line, when the number of particles becomes large. Consider 2k non-intersecting Brownian motions, all starting at the…
We study a simple microscopic model for the one-dimensional stochastic motion of a (non)relativistic Brownian particle, embedded into a heat bath consisting of (non)relativistic particles. The stationary momentum distributions are…
In a celebrated paper, Dyson shows that the spectrum of an n\times n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge…
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…