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We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem…
This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of…
We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
We suggest a new Hamiltonian lattice approach, using a regularisation motivated by deep inelastic scattering. We discuss the relation between distribution functions and the $F_1$ structure function. We have tested this method by computing…
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…
We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator estimates, we gain the existence and uniqueness of…
We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability of smoothness is computed as a product of local…
In this paper we analyze the narrow capture problem for a single Brownian particle diffusing in a three-dimensional (3D) bounded domain containing a set of small, spherical traps. The boundary surface of each trap is taken to be a…
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
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.…
We study smooth linear spectral statistics of twisted Laplacians on random $n$-covers of a fixed compact hyperbolic surface $X$. We consider two aspects of such statistics. The first is the fluctuations of such statistics in a small energy…
Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper,…
A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial…
Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper…
Using the spectral decomposition of the Laplace-Beltrami operator we simulate fractal surfaces as random series of eigenfunctions. This approach allows us to generate random fields over smooth manifolds of arbitrary dimension, generalizing…
A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…