相关论文: Quenched asymptotics for Brownian motion in genera…
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form, involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar…
We find a representation of the integral of a Gauss-Markov process in the interval [0, t], in terms of Brownian motion. Moreover, some connections with first-passagetime problems are discussed, and some examples are reported.
We consider the persistence probability for the integrated fractional Brownian motion and the fractionally integrated Brownian motion with parameter $H,$ respectively. For the integrated fractional Brownian motion, we discuss a conjecture…
Directed transport of overdamped Brownian particles driven by fractional Gaussian noises is investigated in asymmetrically periodic potentials. By using Langevin dynamics simulations, we find that rectified currents occur in the absence of…
We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a…
Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The…
We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis…
Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases.…
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…
Stochastic motion of charged particles in the magnetic field was first studied almost half a century ago in the classical works by Taylor and Kursunoglu in connection with the diffusion of electrons and ions in plasma. In their works the…
It is well known that path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers.…
Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum…
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady…
We investigate the asymptotic behavior of solutions to a second order differential equation with vanishing damping term, convex potential and regularizing Tikhonov term.
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…
We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Brownian motion by exponentiating the square root of the local times of small circles. We also consider a flat measure supported on points…
We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…