相关论文: Gaussian lower bound for the FIN diffusion

The recent discovery that faint gamma-ray bursts are stretched in time relative to bright ones has been interpreted as support for cosmological distances: faint bursts have their durations redshifted relative to bright ones. It was pointed…

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

We address propagation and entanglement of Gaussian states in optical media characterised by non-trivial spectral densities. In particular, we consider environments with a finite bandwidth and show that in the low temperature regime: i)…

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise…

We present a simple argument leading to a fundamental minimum uncertainty in the determination of times. It only relies in the uncertainty principle and time dilation in a gravitational field. It implies any attempt to measure times will…

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The…

We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

In this paper, we propose a novel numerical scheme for solving time-fractional reaction-diffusion problems with Robin boundary conditions, where the time derivative is in the Caputo sense of order $\alpha\in(0,1)$. The existence and…

We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.

We develop and analyze a covariant FO probability valid for a finite space-time layer.

A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…

This article presents a finite element scheme with Newton's method for solving the time-fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank-Nicolson scheme based on backward Euler convolution…

We argue that there is a lower bound of order $10^{-19}$ eV on dark matter mass if it is produced after inflation via a process with finite correlation length. We rely on non-detection of free-streaming suppression and white-noise…

We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the…

We give upper and lower asymptotic bounds for the left tail and for the right tail of the continuous limiting QuickSort density f that are nearly matching in each tail. The bounds strengthen results from a paper of Svante Janson (2015)…