Related papers: Skew Brownian diffusions across Koch interfaces
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$. Assuming the data in question is invariant under an…
Brownian motion in confinement and at interfaces is a canonical situation, encountered from fundamental biophysics to nanoscale engineering. Using the Lorenz-Mie framework, we optically record the thermally-induced tridimensional…
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
We obtain an explicit formula for the full expansion of the spectral action on Robertson-Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman-Kac formula. We then apply this result to…
Brownian motion on a smash line algebra (a smash or braided version of the algebra resulting by tensoring the real line and the generalized paragrassmann line algebras), is constructed by means of its Hopf algebraic structure. Further,…
This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and joint characteristic functions. We provide an alternative…
Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two…
The diffusive motion of overdamped Brownian particles in tilted piecewise linear pontentials is considered. It is shown that the enhancement of diffusion coefficient by an external static force is quite sensitive to the symmetry of periodic…
We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle…
We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic…
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…
We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to…