Related papers: Gaussian lower bound for the FIN diffusion
We prove a lower bound on the first eigenvalue of the fractional Dirichlet-Laplacian of order $s$ on planar open sets, in terms of their inradius and topology. The result is optimal, in many respects. In particular, we recover a classical…
We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any…
In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
The remaining min-entropy of a secret generated by fuzzy extraction from a Physical Unclonable Function is typically estimated under the assumption of independent and identically distributed PUF responses, but this assumption does not hold…
We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding-Lee-Peres and Ding. The estimate is asymptotically sharp as the ratio of hitting time to cover…
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for non-local delayed reaction-diffusion equation.
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…
We propose a Generalized Finite-Differences in the Frequency Domain method for the computation of photonic band structures of finite photonic crystals. Our approach is to discretize some fundamental domain instead of a single unit cell,…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
The mutual information of a discrete time memoryless Rayleigh fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information except the fading statistics. We present the…
The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability $F(g)$ of a general time-inhomogeneous diffusion process to perturbations of the boundary $g$. We prove that, for boundaries $g\in C^2,$ this…
We present an exact expression for the mean exit time through the cap of a confining sphere for particles alternating phases of surface and of bulk diffusion. The present approach is based on an integral equation which can be solved…
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…
In this paper, we study the global existence and uniqueness, Gaussian lower bound, and moment estimates in the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard potential ($0\leq \gamma\leq 2$) with angular cutoff…
In this paper, we present nontrivial upper and lower bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel and identify several ranges of channel parameters where these bounds coincide with useful intuitions.…
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…
In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its…