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In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using…
We provide a simple algorithm for construction of Brownian paths approximating those of a L\'evy process on a finite time interval. It requires knowledge of the L\'evy process trajectory on a chosen regular grid and the law of its endpoint,…
By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some…
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…
We propose a numerical method to compute the inertial modes of a container with near-spherical geometry based on the fully spectral discretisation of the angular and radial directions using spherical harmonics and Gegenbauer polynomial…
Gradient optimization algorithms using epochs, that is those based on stochastic gradient descent without replacement (SGDo), are predominantly used to train machine learning models in practice. However, the mathematical theory of SGDo and…
In this paper, we develop a Young integration theory in dimension 2 which will allow us to solve a non-linear one dimensional wave equation driven by an arbitrary signal whose rectangular increments satisfy some H\"{o}lder regularity…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the…
We investigate the kinetic Schr\"odinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schr\"odinger's thought experiment. Under a quasilinearity assumption we establish exponential entropic turnpike…
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic…
We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time…
In 2001, Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a…
We propose an efficient numerical approach to simulate the boundary local time of reflected Brownian motion, as well as the time and position of the associated reaction event on a smooth boundary of a Euclidean domain. This approach…
We study the asymptotic properties of an estimator of Hurst parameter of a stochastic differential equation driven by a fractional Brownian motion with $H > 1/2$. Utilizing the theory of asymptotic expansion of Skorohod integrals introduced…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…